Hello all. New to working on my bikes and I had a question. I want to change the cassette on one of my bikes to something a bit better and am soliciting any advice for doing so. My bike currently has a 14-28 cassette and a Shimano Tourney derailleur (see pictures). I want to install something like a 11-32 or at least 11-28.

1. Do I also have to change the chain?
2. Any difficulties to look out for or special tools needed to change the cassette?
3. Will the existing derailleur still work? Is it compatible (reach) with new cassette?
4. Anything else I should know before attempting it?

I attempted to post a photo but due to my new status to the forum was unable. I hope I have described the situation well enough.