Does this white pagani design 1682 have a nh35a seiko movement?

Pagani watches with automatic movements usually have Japanese movements similar to Seiko automatic watches.

Does the bracelet taper down from 20mm to 16mm?

It tapers down for sure just don't know the exact amount. Nice watch just big for a smaller wrist.

What causes the watch stop running?

Because this is an automatic/mechanical watch you must either (1) manually wind the stem [20 times] or (2) steadily shake the watch horizontally to trigger the movement prior to placing it on your wrist. On average an automatic watch has a duration ranging from 30-42 hours. An automatic watch depends on the charge level (as determined by the wrist movement) of the rotor vs a purely mechanical movement which depends on a spring. For this reason if you only wear the watch a short period of time during the day then the duration will be shorter.

I understand that the bezel does not rotate. how do you set the hand for the proper gmt time?

The GMT complication works perfectly, but it is a little tricky to find the right spot on the stem to adjust. One direction advance the GMT hand, the other the date. Pulling stem fully out hacks the second hand and provides minute/hour adjustment.