Can I see all Apple ID on my iPhone

There can only be 1 iCloud account set up on the iPhone at any on time. It can be seen in Settings->Account(top of settings) under your name and picture. The logged in account's email address will be shown there for iCloud and iTunes & App Stores. If you only see one account/ address there, then both things are signed in to the same account.

You can also go to Settings->Messages->Send & Receive->Apple ID, and Settings->FaceTime->Apple ID, Settings->iTunes & App Stores->Apple ID to see what account is signed in there.

No you can't do that.