It seems that only the neutral races are open with F2P - are those their own side? meaning it's Good vs Evil vs Neutral? if that's the case... isn't neutral like overflowing with people since those are the F2P races?

the starting city you choose - determines if you are good or evil

It really does not matter at this point.  The starting cities of freeport/quenos have been gone for years.  You start at Gorywn, New Hallas or Neriak,or that faye area now.  So you have 1 evil, one good, 2 neutral.  Certain races you have to pay to unlock, or go gold.  

Also a long time ago race did matter in pvp,but that all changed years ago as well.  Used to be you chose certain races to be certain arca types like scout,tank,healer,utility.  That also changed as well as a lot of the racial abilities changed too.  However some races do better but really after the racial changes the benifits you get are not as great as they were back before the velious expansion.