What is the market share of non touch mobile browsers? How many percent users use those browsers?
This is generally region dependent so it depends on your audience. You can get some idea from
https://deviceatlas.com/device-data/explorer/webusage-by-country/traffic/mobile/country/us/type/browser_name
http://gs.statcounter.com/#all-as-ww-monthly-201610-201612-map
But in my experience these are not very helpful because a lot is determined the type of customer your product focusses unless it is a very widely adapted product on e.g. On an niche e-commerce site selling high value stuff you will find Safari prominent. So before solving the problem if you can collect some data (if you have existing product) or ask in forums/fb groups to people who have a product in a similar domain, it will help you in prioritizing, because building is a smaller issue than maintaining it.
I have made my whole website with bootstrap assuming touch functionality for small screen devices. Does modern day html css best practices suggest making website only for touch enabled mobile devices?
Edit: Upon listening to the suggestions I have decided to optimize for non-touch mobile devices too. But I am not sure how they mimic mouse behavior in general. I am guessing that elements that are focusable can be selected and clicked. So,
If you want to cover wide range of browsers use https://modernizr.com to detect features and respond accordingly or have fallback interactions. Caution, it's always not a good idea to pull a library if you want only few features, so see your use cases. On the other hand the advantage is it keeps getting updated.
You can see the list of touch (and similar) events fired by different browsers here http://www.quirksmode.org/mobile/tableTouch.html#link1
For list of apple non-touch events take check this
https://developer.mozilla.org/en-US/docs/Web/API/Force_Touch_events
Similarly you will have to dig for event lists for browsers which you want to support.
Should I make all my elements that work on hover, e.g. the navigation, focusable with tabindex = "1"?
For tabindex what Andre suggested is right (have the right order for important elements, which should be done at testing stage).
Check this to get an understanding when to avoid and cases where it can create an issue. There are more than the ones listed here, so do a good research if you are playing too much with tabindex.
https://developers.google.com/web/fundamentals/accessibility/focus/using-tabindex
I have been testing my site on opera mini browser in Kemulator and found that it reloads page when I click on navigation and some other layers are not shown, e.g. the bootstrap modal pop up.
Does opera mini browser not support javascript well?
In most cases Opera Mini processing is done via Opera servers, which often prevents JS from working correctly.
These are the workarounds for some features, for which you can refer to https://operamini.tips/#/
All being said, still I would suggest, do a good target user research, and from there prioritize your list of support for your initial versions. It may require investment of time and maybe some money too but it is totally worth it. Then improve on the shortlisted ones till you are able to remove major bugs, and when you have bandwidth then attack the next part of the list. Having an approach of supporting too many browsers/devices/screens at first will take you down the "support labyrinth" from where you will be stuck with removing bugs everywhere, and feature development will go out of focus.
Also integrate GA analytics (or any other) well and attach events to major interactions, and keep monitoring according to screen sizes, device and browsers. e.g. Opera Mini gives me 0 events in some pages and that raises an alarm. Sometimes it may not be 0 but a low ratio of users who interacted /users visited. You can attach events with scroll, field select etc. Prioritize first on major features of your product, track, choose what to focus on, improve, test and then move to next part. So basically this will form a matrix of features with browsers/screen sizes and then prioritize accordingly depending on your traffic type.
there are very few browsers that still use < 800px
? You can always resize your browser to fit only portion of screen. Why everyone thinks that you always use browser in maximized mode? – Chandelier