AFAIK there isn't much of a style guide beyond a few simple things listed here: https://coq.inria.fr/cocorico/CoqStyle. Some people (e.g., Adam Chlipala in his book "Certified Programming with Dependent Types") advocate automating proof scripts as much as possible by writing a lot of custom Ltac, but that's more about development methodology than style.
Encouraged.
Probably at least the things described in the link above.
No linter that I'm aware of.
In the Coq projects I've contributed to, the files are all lower case with no underscores or anything. However, the files provided for the "Software Foundations" textbook (a popular book for learning Coq) all begin with a capital letter.
Note that this is about the exercises (the test suites and code examples), not people's solutions.