name of the part
It's called a "seat belt retractor". Different part numbers for different years and different part numbers for coupes and sedans. New they are $75-100 each. Check out Ed Morad
Morad Parts Company - 3800 Motors, Transaxles, & Stock Parts for an economical replacement if you don't want to hit a local salvage yard.
will it come with that panel? If not, where can I get a new one?
No. Console and the Trim Plate Assembly are two seperate parts. Console is the same for all years (97-2002), Trim Plate shows three part numbers (97-99, 2000-01, 2002). Console is $75.50, Trim Plates are $98. Once again Ed Morad can probably fix you up MUCH cheaper. He's saved me hundreds.

Note: My prices are from 2003 so they are almost certainly low.

anyway to know the car is going into performance mode.
The button on the shift knob changes the shift points of the transmission. It will hold in a gear longer when the button when you're in performance mode then when you're not.