พูดอีกที

By itself, it's informal. Add 'khrap' or 'kha' to make it polite.

'Phut ik thi' is 'Say it again', 'Phut mai' is 'Say it anew'. They are mostly interchangeable.

Yes, but use the full polite form: 'Rop-kuan phut ik thi dai mai khrap?'

Use 'Phut cha-cha' (พูดช้าๆ).

'Arai na' is shorter and more common in very casual settings, like 'Huh?'

Yes, in the sense of an 'occurrence' or 'turn'.

Yes, that is the formal version often used in speeches or writing.

Say 'Khor thot khrap, yang mai khao jai' (Sorry, I still don't understand).

'Wa ngai na?' is a very casual/slangy way to say 'What did you say?'

It's a falling tone. Start high and drop low, like you're saying 'No!' firmly.