Pronunciation question, please help?

In "right" and "what", your tongue ends up behind your upper central teeth so "T" is voiceless. The "P" endings have your lips together, and most people voice the "p". A few do not.

No. Those consanants, when in initial position are "stop plosives"; there is a slight "puff" at the end of the sound. In other positions (medial, final) this "puff" doesn't happen, so this sound is a "stop" but not plosive.

You may hear a different pronunciation is emphatic speech, especially in interjections: What?!