On Moderate I was always underlevelled in the latter half of the game, personally. Partially because I was so sick of the dungeons that I started running through them at a faster pace.
The problem I find with bosses isn't inherently that they're tough or anything. It's just if you play your cards wrong you can lock yourself into an unwinnable situation on certain fights. When bosses get below a certain hp threshold they often do a kind of "soft enrage" I noticed where they'll start spamming moves. Now that's fine if you have enough souls yourselves to be doing shit, and the enemy doesn't have much. However if the boss has 5 souls, and you don't have enough souls to be distracting/stunlocking the boss a bit to keep them occupied you can have this problem where they spam the shit out of their heavy hitting spells/attacks which cover half the battlefield, and devastate your party while you can't do much to stop it. Due to them having 5 souls, casts go off almost instantly, and sometimes attacking doesn't interrupt casts anyway. So you can be in an endless cycle of party members dying (the AI is, as per usual for a Tales of game, useless at getting out of AoE), you trying to get them back up, only to have other people dying. If that happens, you're frankly better off just letting yourself get a game over, instead of trying to fight through, and just make sure you don't make the same mistake again.
TLDR: It's fine to be under-levelled you just have to be a bit more careful, as spells/attacks will be more likely to kill you. As long as you manage your souls/resources and take advantage of weaknesses/stunning/status ailments you'll be fine.
I believe so, yes. Normal is the default level. Simple makes the levels lower, anything above Normal makes the levels higher.
You also technically get less EXP on higher difficulties too. Though the EXP multiplier increases.