1. Current content is personal loot and you have an increased chance of getting it because each toon has a chance since most mounts are battle.net bound.
2. You asked two questions here and one is No and the other is Yes. No you don't get 5 chances if grouped up. You always run legacy 5man/raids as solo to increase the chance of mount drops. It's just like any 5-man/raid where loot drops for the entire group and all toons will be locked to that instance and can only try once. If your character is 11 levels or higher than the content, then legacy loot mode is enabled, not personal.