Can you take Pre-med classes at a CC instead of a 4 year uni and still get into a good Med School?

That would be a silly move, and likely impossible anyway. Why would you leave a fine, respected university like USF for Berkeley???

While at USF, you’ll get to know your profs, get research opps, etc. Why ruin that an transfer to a big school where no one will know you??? Besides, UCB takes very few non-CC transfers.