1. You will only be able to buy weapons and items from the online shop, and you will not be able to forge. However, you will still be able to reclass. You can only select units from one file, I'm afraid.
2. Items and weapons can break online. They'll start with whatever uses they ended with during the main adventure, and it's reset to that number after each wifi match.
Here's just some extra advice;
I would recommend making a seperate file specifically for building a wifi team if you haven't done so already. Plan out the team, their classes/weapons, who will likely be getting the stat boosters, etc. The best classes from class set A are Swordmasters, Snipers, and Paladins/Falconknights for tanking/scouting purposes. Class set B's classes of choice are Horsemen and Berserkers. Every teams needs a Sage/Sorcerer as well.
Arena abuse like heck in a wifi file. All weapons brought into wifi with the exception of the Gradivus should be forged with maxed power, good hit, and crit if you're not using a Dazzle card. As you can imagine, you'll need a lot of money for that. Keep in mind that Brave weapons are sold in the online shop on weekends, and it will take you a month to get a complete set of them. Make every weapon/item slot count. If you're giving a forged Brave Sword to someone, don't bother giving that unit a Silver Sword or something just to fill up space. Instead give a forged Armorslayer, Wyrmslayer, a Pure Water...anything that might be helpful.