Currently we're using Django admin extensively and I wonder if it's possible to continue using it once the monolith is broken. It means reading and manipulating data from all the microservices in a "used to work on" UI. It would also be helpful for this process to be done more smoothly.
Yes, you can but it may not access the other microservices databases (neither write nor read). This means that if the Admin microservice update some Article (or whatever entity types you have, this is just an example) then this is not reflected immediately in the microservice that displays that Article. You need to have some mechanism to transfer the updates from the Admin to the other microservices. So shared databases/tables is not an option.
Authentication and authorization - Would we still be able to use this built in "app" in a microservice architecture? Is it possible to take this pare only to another service and communicate with it over HTTP?
Yes, but you need to split it into two sides. One side is responsible for managing users and roles/permissions and the other is responsible to authenticate the users and to check if a user may perform some action.
The first side should be a microservices (the creation/administration or users and the managing of roles/permissions).
The checking part can be a microservice but those responsibilities are in general taken by the API gateway or by a module (+ local, replicated data) in every microservice that need authentication or authorisation. These are cross-cutting concerns. If they reside in a separate microservice then there is the problem of resilience: if that microservice fails then it brings down you entire system.