1. So what mining program actually mines bitcoin? Please answer with a link. I've googled this to death only to find programs that mine cryptos other than bitcoin
CGMiner[1], BFGMiners are all suitable mining softwares. You need a Bitcoin ASIC to mine Bitcoins with those program, I think GPU support was deprecated. Since Bitcoin has been dominated by ASICs, it isn't viable for anyone to be using their own computer to mine and expect to gain possibly a few cents a year.
2. Why is it when I exit a mining program after I've been mining for an hour, that I lose video feed from my GPU and I have to force a reboot of my PC to get video feed from my GPU again?
(and no, my GPU/CPU hasn't been overtaxed). The warmest temps I got from my CPU/GPU is (50c/61c) for nicehash and (51c/66c) for EasyMiner.
What's your driver version? Can you try reinstalling it?
Just got my first payout from nicehash. I just figured out that even though I was mining mBTC for some reason, I was paid in BTC. So it looks like I managed to make 0.00001102 BTC which I think is worth .61 in USD. That represents about 2 hours worth of mining total of what I did yesterday, using both my GPU and CPU if my math is right.
Did some math and if my math is right, I'm mining .305 USD/hr on my PC, which means if I let it run for 24hr, I'd be making 7.44 USD per 24 hour period. Does that sound about right to you experienced miners out there, or is there a better way to mine, using what I have?
You probably didn't mine Bitcoins. You're instead mining altcoins, possibly Ethereum and it was converted automatically for you through NiceHash. You can possibly try to search for parameters pertaining to your GPU online that would optimize your hashrates, undervolting, etc. I've never used NiceHash as a mining client but I've had experiences with PhoenixMiner[2], beware of malware links around.
[1]
https://bitcointalk.org/index.php?topic=28402.0[2]
https://bitcointalk.org/index.php?topic=2647654.0