Answer 1

I made a rock paper scissors game and a dice rolling simulator as my first projects - they were pretty easy to code and good starters

Answer 2

you can pretty much do everything other languages do . Python is a very powerful language and it is used a lot , there is "almost everywhere"

Answer 3

I personally think a good intermediate program would be a solitaire type game, or poker, like Texas holdem. I feel it incorporates a lot of math functions and object oriented principals that should help hone your skills.

It also allows you to go through a discovery process that most projects require to gather what the program has to actually do, before even beginning the first line of code.