Most battle leve can be done in a party; my fiancee and I duo our classes up between dungeons/fates/leves with the guildheists as we went up for the bonus completion xp. That said, Leve's can also be done with your chocobo out. The only ones that can't are gathering and crafting leves. It will also not allow you to leve while a party member is in a different zone or instanced.
The character your posting under is a level 50, so you'll have a 50% bonus XP on every kill (up to 100% if also under rested xp) all the way to 50 on battle classes. if you're talking about an alt character, you'll get the 50% bonus upto the highest level you currently have. if your 20, everything gets the bonus to 20.
My fiancee and I just unlocked the Challenge Log, it can give massive xp while leveling. I'm loving it on my goldsmith and miner atm.

We went from 20-50 in about 3 weeks, only playing 17 or so hours a week; without rested xp/with challenge log