Strategy to exercise OTM options after market close on Expiry Day (becomes ITM after hours)

Say I have 50x of NVDA Call option $200 strike price

market closes on expiry day at $199 = worthless and will not be automatically exercised,

but then price increased to $202 after hours at 4:10pm ET, becomes ITM.

I only have $100,000 left in my balance / purchasing power including margin,

and intend to exercise the option + sell shares immediately.

1. Does that mean I can only exercise about 5 options (out of my 50 options) ? Since I will only get assigned the next trading day, should I sell the shares first, or exercise it first (is there a feature to do it simultaneously) ?
2. After doing both transactions, would both positions be closed immediately (and I'm left just with the profit), or would both positions still show in my dashboard until next trading day?
3. Since exercising call option + selling underlying shares, kind of cancel each other in terms of my purchasing power (does the broker e.g. IBKR see it this way at 4:20pm?), can I rinse and repeat this every minute, 5 options at a time, 10 times, so that I can utilize all my 50 options?