How can same machine take same machine as input(is it same machine taking encoding of itself as input—if that’s the case, what does that means some examples to understand this)?  (in Universal Turing Machine, i know it was possible). What does that even mean here?

 

I feel like adding a turing machine flipper is like cheating and should not be allowed as well.

 

 

Your links are broken, I'll try to respond anyway.

1. Consider a game console. There exist game console emulators, and there's no theoretical reason that a game console couldn't run an emulator of itself.

2. Why? It's consistent with the problem.