Yep. I think the next replacement should be the mechanic. Sounds like he went to the "Replace to Repair School". The question is when does he get down to replacing the engine and transmission? Has the guy run a dipstick through your bank account yet?
And yes, absolutely you can do a most of the fluid level checks yourself, from oil to transmission fluid, brake fluid, coolant, etc. All you need is a clean rag and a copy of your car owners manual that you should have gotten with the car. Just take a look in the index. And if you want to become a little more knowledgeable, proactive and increase your wow factor at the garage or shop, you can probably get a Chilton or Haynes repair manual from these guys:
http://www.discountautorepairmanuals.com/ for ten bucks or so.
There's a lot of maintenance you can do yourself and a lot of fault or trouble shooting by following the tips in those well-written, easy to understand manuals that have lots of pictures to help. You can go to the "Find a Mechanic" feature on this site at the home page on the right hand side.
There's a protocol of questions, answers, and system checks mechanics follow to isolate and diagnose problems. While yours might be as simple as a transmision fluid refill, fluid and filter change or band tightening, these things are easily checked before doing any replacing. It could also be a dirty fuel or other filter. Proper diagnosis is the key and it's a fairly straightforward process.