Yes, a single character can have every class and job at max. There aren't enough quests to level every class purely through quests. That's where things like the hunting logs, challenge log, levequests, FATEs, guildhests, dungeons, beastmen dailies, and roulettes come in. It's not difficult leveling a class when you have no quests left. It's just less questy.

Bonus attribute points are per class. So your GLA/PLD can go for all VIT, and your THM/BLM can go all INT. The only jobs where it's currently a thing are Scholar and Summoner, since both have Arcanist as their base class. SCH wants MND and SMN wants INT, so it's either split the points 50/50, choose one and leave the other a little less than optimal, or buy attribute reset items from the Grand Company to reset all the time.

You can't send your other characters anything through the mail. You can have them in the same FC and use the FC bank (assuming you have the bank privileges to do so and trust the rest of your FC that much), you can use a trusted (and incredibly patient) friend to pass things back and forth, or (if the items are market-boardable and you have the funds), you can sell your stuff to your other characters on the market boards for stupid high prices that you know won't get bought in the meantime.