It sounds like a good experience. I won't lie, I don't like your play on the hands mentioned above, but it sounds like you identified the key hands that you would have liked to have played better. Truthfully, they were all mucks. Here is some quick stuff, to consider.
Cash games are not tournaments. There is no pressure from rising blinds. In a cash game you are looking for specific strategic situations, you only need to win 2 hands a session, choose them wisely.
The average min hand required to win is 2 pair. Top pair top kicker is something you have to get away from once in a while. Forget second pair completely.
Your sixes Im guessing was a blind steal. Not bad maybe you got caught with your hand in the cookie jar. When they popped it up behind you, well you tryed got caught tap the table say nice hand, and muck it. Even if they are restealing, just throw it away.
The threes ugh a minor tilt? you mentioned you were tired of being pushed around.
You were definately card dead. If those were the spots you chose to make a move with, then better cards are in your future.
Plan on rebuys in cash games you should theoretically never be down in chips because you can reload anytime. Reload, or take your chips to the cage. If your short in a cash game, when you finally pull cards, you can't get paid in full for them.
Hang in there we all go card dead!