Do you pronounce the T sound when saying "What?"?

When the word stands by itself in conversations, most people indeed to pronounce it but you don't actually hear it because most people don't pop the final T sound.

Now, when it's connected with a word that starts with a -y sound (like this case, what's your..), the t's part makes that -s sound as in pleasure/treasure, at least in relaxed North American speech.

Hahah, that's a good question...I never really thought about that.
Generally it's just soft, but if you're saying "what?!" for emphasis, then you can.

sometimes

Usually as a tap or glottal. I'd certainly never aspirate it. Realizing it as a dental stop there tends to be highly emphatic in American English.

in a : i pronounce the T clearly
in B: is depend the kind conversation like whaaat ??! i don't use T clearly

No, softer T. If you say it really quickly a bunch of times with a soft D sound at the end you'll know how to say it. "wud's your name? Wud's your name? ..."

Yes; check the US Dictionary, the phoenix shown as below, which shows the sound of T:

what |(h)wət; (h)wät|

No. But maybe because I'm Australian.