The fastest way to gain EXP is either do quests or kill higher level monsters with Chain Attacks. I'm not sure what level you are, what Blades you got, etc. so I'm not sure how feasible it is to rely on Chain Attacks to boost your EXP gain. Once you master Chain Attacks, elemental bursts, etc. you can get 1000 EXP from regular enemies and 3000+ EXP from Unique monsters. I went from 32 to 50 in basically a day.
You can put items (food, board games, art, books, etc.) in your pouch to give you a boost during combat. You gotta read what the item does though. Also a lot of Blades have favorite items (for example, Pyra's is Jenerossi Tea) and if you use them it raises their skill levels.
1. See above.
2. You find Confusion Ivy in Gormott. Check every Collection Point near trees.
3. Yes, do every side quest you find. It's basically free EXP.
4. Use every Core Crystal you find....they're mostly going to be trash. You'll get Rare Blades but it's basically just luck.
Around Chapter 3 or 4 you get a mercenary company and you can send random Blades on missions for treasure, EXP, etc. That's another way to gain EXP.
Also don't forget to sleep in Inns. You can level up off killing monsters but you get EXP from quests and it adds up and can be "spent" at Inns when you rest. I went from 46-49 just off resting in Inns.
5.
Fred.