"I have done a lot of reading and taken several college level courses. There are some major problems with evolution in my mind.
1. The origin of life on earth. (presumably prokaryotic cells in a non oxygen containing atmosphere)
2. The origin and evolution of DNA.
3. The evolution of the eukaryotic cell.
There are some other technical problems concerning the fact that some animals aren't well adapted to the environment that they exist in."
You are not being honest with your questions. Both #1 and #2 are not part of the TOE, as you well know. If you want to question current thought concerning Abiogenesis, that's fine, but it does not impact Evolution. #3 Is well understood, if you will consult any good cell biology text.
The adaptation question is quite simple. I'd ask you to ask yourself, if you will. Organisms don't have to be "well adapted" to their environment, they just have to be successful. The crunch comes when there is competition in that environment or when it is invaded by a "better adapted" creature. Then change either occurs or one species is either marginalized or becomes extinct. Happens all the time.
Well Watson chose to bring up the subject of DNA in an article on Darwin. Now we can't ask how it evolved? Also doesn't DNA's ability to replicate itself depend on RNA and how did these two co-evolve?