What I have been doing so far is keeping all my Pokemon at the same level, switching my lead whenever my current lead levels up. My question is, A. Is this a good idea and B. Will my pokemon level up enough through trainer battles without having to grind in order to beat the game?
Yes it is a good idea. 90% of the time you'll be a bit underlevelled for the E4, but this is normal. You could still beat them if you play on their weaknesses.
Also...on a side note...I made a HUGE mistake in teaching my starter pokemon an HM move without realizing I couldn't take it off, and I now I am loosing abilities that I want because of it. I read online there is a move deleter, but how far away am I from reaching that (I have 3 badges to give you an idea of where I am)?
The Move Deleter's in Canalave, which you can access after getting the fifth badge. So it's not that far, I guess. Depends on how far you are from getting your third badge.