What year and model?
Selecting neutral can be a real pain on early 2000s, even with the engine not running. To get into neutral while running, you'll have to let the bike move forward after selecting neutral, which is usually easier to set from 1st, half a click up. To get into neutral with the engine off, you often have to push the bike forward while in gear. This I think makes the drum rotate (don't kill me if I am wrong).
As for the drag, did you bleed the line? Change the oil? Make sure the clutch lever engages all the way? Mine used to drag a little bit, nothing serious, but when it was cold I had to rev a bit before pushing into 1st.
I bled and changed the oil (plain baby oil works). I also changed the master cylinder as I broke it in a fall, and I replaced the OEM lever with a CSV lever, which can be adjusted to push a bit farther into the cylinder than the OEM. Start with those easy checks and fixes. No more drag in my case.