Here's a (long) alternative answer. Note that I used to recommend Stack for beginners, too, but I've since changed my mind.
TL;DR: Either Haskell Platform or a pure Stack installation can provide you with everything you need, and you won't be "missing" anything by choosing one or the other. You'll probably find it easiest to skip Stack and install Haskell Platform using the "Generic" Linux installer, because it comes with everything you need and the setup will more closely matched what's described in the LYAH book. You can install Stack later when you're doing more serious development on multiple projects. If you prefer to stick with a pure Stack installation, I'd suggest starting with a "global project only" workflow. Either way, you can use "haskell-mode" with some configuration fixes suggested below (including a key setting that will be required if you're working in the global project of a Stack-only installation).
Here's the long answer...
Stack vs. Platform vs. Cabal
The LYAH book pre-dates Stack, which is certainly the main reason it doesn't mention it. At haskell.org, they recommend using either a minimal installer, Stack, or the Haskell Platform. All three methods are perfectly reasonable ways in 2018 to set up a working Haskell environment. They differ both in the ways they choose to isolate different versions of the compiler and/or libraries into "sandboxes" for development work, and in how much they install initially, but there's nothing "missing" from any one of them that can't be installed on demand. Depending on which you choose, there will be some differences in your workflow (see below).
Both Stack and Cabal are combined package managers and build tools. (Stack has the added ability to actually bootstrap an entire Haskell installation, which is why it's also an installation method in its own right.) While you're working through LYAH, you won't actually be using the "build tool" functionality directly on your own projects. (The built-in build facilities of GHC are more than adequate for building small, multi-module projects.) You'll just need the package manager functionality to install additional libraries.
Since Stack and Cabal manage their packages separately, if you're using Stack, you'll have no particular need to use Cabal directly. You can install it if you want (and in fact, Stack makes use of Cabal for some esoteric functionality, like "stack solver", and will require it to be installed in those cases):
$ stack install cabal-install
But, even though this will put "cabal" into "$HOME/.local/bin" (and you'll want to make sure this is in your path), you'll find that you need to jump through hoops to run it:
$ stack exec --no-ghc-package-path cabal -- list
and it doesn't really do anything useful as far as your Stack environment is concerned.
Update: A note on the "$HOME/.local/bin" path. It looks like the installation script from https://get.haskellstack.org/ may install Stack itself to /usr/local/bin/stack by default if there's no existing installation. However, it should display a warning to put $HOME/.local/bin in your path. If you upgrade Stack in the future with stack upgrade, it'll install the new version of stack there, and that directory will also be used if you install packages that include binaries. For example, stack install hlint will install the Haskell Lint program hlint to that directory. So, it's a good idea to have it in your path and somewhere before /usr/local/bin.
What's Missing with Stack
I think that covers your first three questions. For your last, the main thing you're missing having installed Stack instead of the Haskell Platform is that, by design, Stack doesn't really install anything globally other than "stack" itself. So, all your Haskell work including running the Haskell interpreter ("ghci") or compiler ("ghc"), all needs to be done within a Stack environment, either using a specific corresponding Stack command:
$ echo 'main = putStrLn "Hello, world!"' > Hello.hs
$ stack ghc -- Hello.hs
[1 of 1] Compiling Main ( Hello.hs, Hello.o )
Linking Hello ...
$ ./Hello
Hello, world!
$
or else using "stack exec" to run a generic program within an appropriate Stack environment. For example, it can sometimes be helpful to run a Bash shell under stack, after which things behave sort of like a globally installed Haskell Platform environment:
$ stack exec bash
$ ghci
GHCi, version 8.2.2: http://www.haskell.org/ghc/ :? for help
Prelude> :quit
$ ghc -O2 Hello.hs
[1 of 1] Compiling Main ( Hello.hs, Hello.o ) [flags changed]
Linking Hello ...
$ exit
$ ghc
The program 'ghc' is currently not installed. ...
$
The other thing you're missing is that the Haskell Platform installs a whole bunch of common libraries by default, while a fresh Stack environment starts with almost nothing (not even the compiler, before you run stack setup). While working through LYAH, you may find you need to periodically install additional libraries. For example, in the Input and Output chapter, the examples using random numbers (module System.Random) will require you to run:
$ stack install random
and restart your interpreter.
Recommendation to Use Haskell Platform
Because Stack is a little complicated and you won't really need the facilities it provides at the beginning, you may find the Haskell Platform easier to use when you're starting out. (The "Generic" installer should work fine on your distribution.) It comes with everything installed, and the way you use it will more closely match the way things are described in LYAH. Together with haskell-mode, you should have a pretty decent Haskell environment.
In general, there should be no issue having Stack and the Haskell Platform installed side-by-side (as evidenced by the fact that Haskell Platform actually includes Stack). Stack will maintain everything separately under the "$HOME/.stack" subdirectory, so there will be no interference between compilers or packages or anything. Note that in this setup, you'll use cabal to manage the packages installed on the Platform side of things, and stack -- obviously -- to manage packages on the Stack side.
Beginner Workflow for a Pure Stack Installation
If you want to stick with your pure Stack installation, I might suggest the following workflow when you're starting out:
You will see references to Stack projects, created with "stack new" or "stack init". Avoid these at the beginning, and stick with the stack "global project". This is the implicit project that will be in effect when you run "stack" in a directory that doesn't have a "stack.yaml" file (directly or in a parent directory):
$ cd
$ stack path --project-root
/u/buhr/.stack/global-project
$
When you're working in the global project (i.e., not somewhere under a stack.yaml file), you can invoke the interpreter and compiler with:
$ stack exec ghci
$ stack ghc -- -O2 Hello.hs
and they will both have access to any additional libraries (packages) you've installed using commands like:
$ stack install random
Updated: A note on the difference between stack ghci and stack exec ghci. The former is intended to run GHCi within the context of a local project (i.e., working under a stack.yaml file). It passes some additional flags to hide globally installed packages and to automatically make available modules from your package. When working in the global project, I don't think there's any practical difference except that stack ghci generates a warning; and no matter which you use, you'll need to load your own modules explicitly with :load Whatever.hs. There's a little more info on the difference on this Stack documentation page, particularly at the bottom where it tries to explain the difference.
Eventually, you may switch to a workflow that uses Stack projects. This will involve using stack new to create a new Stack project directory, stack setup to install/link a private compiler version into that directory, and then modifying the project's xxx.cabal file (and possibly its stack.yaml file) to indicate which additional packages are required, instead of using stack install. It's all a little complicated when you just want to get started writing code.
You may also see reference to Intero, an Emacs mode designed specifically for Stack. Intero is very nice, but it doesn't work very well when working on files in the global project. It'll tend to want to start up the interpreter in the directory "~/.stack/global-project", which is pretty useless. (I use Intero, but I've patched it to behave better in this respect.)
Configuring Haskell-Mode (for Either Platform or Stack)
It's probably best to stick with "haskell-mode" instead, and think about Intero when you start using non-global projects. I'd suggest installing "haskell-mode" from MELPA as per the instructions, but adding the following to your .emacs file instead of what's suggested in the documentation:
(require 'haskell)
;; add capability to submit code to interpreter and mark errors
(add-hook 'haskell-mode-hook 'interactive-haskell-mode)
;; add missing keybindings for navigating errors
(define-key interactive-haskell-mode-map (kbd "M-n") 'haskell-goto-next-error)
(define-key interactive-haskell-mode-map (kbd "M-p") 'haskell-goto-prev-error)
(define-key interactive-haskell-mode-map (kbd "C-c M-p")
'haskell-goto-first-error)
;; merge this with your existing custom-set-variables
(custom-set-variables
;; NOTE: include following line to work around haskell-mode
;; bug if using GHC >= 8.2.1.
;; See: https://github.com/haskell/haskell-mode/issues/1553
'(haskell-process-args-stack-ghci
'("--ghci-options=-ferror-spans -fshow-loaded-modules"
"--no-build" "--no-load"))
;; some options suggested in the haskell-mode documentation
'(haskell-process-auto-import-loaded-modules t)
'(haskell-process-log t)
'(haskell-process-suggest-remove-import-lines t)
;; make sure "stack ghci" is used, even in the global project
'(haskell-process-type 'stack-ghci))
I've tested this with a pure Stack installation using "haskell-mode-20171022.26", and it seems to work fine. I can load a new Haskell file in the global project, submit it to an interactive session with "C-c C-l", and browse highlighted errors in the source file with "M-n" and "M-p". (The errors appear in the mini-buffer.)
If you decide to use the Haskell Platform instead, I think all of this "haskell-mode" configuration will still apply, except you should remove the very last customization line. (The default haskell-process-type of auto will pick something appropriate.)
Hope that helps!
stack ghci. With respect to question 4, a brand new Stack installation includes the core platform packages (e.g.,containers, which does seem to be available in the global project without further installation), but is missing most of the libraries available with the Full Platform (e.g., including some very popular ones likerandom,text, andmtl). – Unbalance