What would happen if I made some minor code edits (ie coins rewarded per block and number of.coins allowed) what would happen if I just compiled and run that with the original genesis block and merkle root of bitcoin. Wpuld I be mining bitcoin or my own coin?
It really depends on the specifics of the particular edits that you make.
If you change your code so that the initial block subsidy is less than 50 BTC, then you might have a problem accepting the Genesis block since it has 50 BTC.
If you change your code so that the initial block subsidy is allowed to be larger than 50 BTC, then your client will download the entire current bitcoin blockchain and you will be mining bitcoin. However, anytime you solve a block, if your miner tries to create a subsidy greater than 25 BTC, the entire network will ignore your block and it will be orphaned, therefor you'll never get the reward.