Can I process my own transactions from my wallet on my miner? I would like to process my own transactions because then I could have my transactions go faster and not have to pay extra because it would be processed locally? I know this might sound dumb but I would still like to know.
The only miner that gets to decide which transactions go into a block is the one that is lucky enough to find the next block. So, yes, if your miner is successful in finding a block, then you get to decide which transactions are included.
If you are mining in a pool, your miner probably doesn't get to decide which transactions get included. The above only applies if you're solo mining.