1. No. Characters don't learn more spells ever, sadly.
2. The resist mechanics are on the game's JP Wiki and in the manual (Which you may have)
3. Chen may have more HP and DEF, but it's still at such utterly negligible levels anything noteworthy will tear her apart. Plus she's got far worse affinities and MND than Patchy (Who, for a good chunk of the game, is nigh-immune to magic).
4. Meiling boasts slightly less DEF than Remilia, but overall her HP, MND, and affinities are notably better - with a defense buff, even some of the most powerful threats can survived with startling ease. Not only that, but her support capabilities (Colorful Rain and Healer) are extremely useful for her survivability (Especially against PSN, which is practically a death sentence early on). Remilia is, however, more capable on the offense.
5. The optional boss on 1F was the first of a string of superbosses originally meant to be fought after completing the main game. Don't worry about em until after beating the main game's final boss on 20F
6. Stats aren't random at all, but it's worth noting, the boosts you give em on levelling/etc are permanent and continuously effective - it's bonuses adding onto a multiplier/percentage value, as opposed to a flat addition. So, if you put 20 level ups with an ATK bonus, you'll have 40% more ATK then you'd normally have at whatever level, according to the base value. As a result, that means more total stat growth by adding onto already high stats, as opposed to trying to raise crappy stats (Which won't do nearly as much)
7. Grinding doesn't matter too much until... about F13 or so, where it starts to matter a bit more. Plus Disk content amps it up a bit... and then F30 is a giant wall of grinding (You'll get there at about level 200 or so, apparently... and recommended level for the uber secret boss is
600), but gives you more than enough ways to get that.
8. Actually... -don't- use Rest unless prepping for a boss. Switch characters into reserve instead and they'll regain SP without losing TP from being in battle. Rest will take TP from everyone - even if they DON'T have SP to recover. It's also worth noting, if you haven't seen yet, that TP will drop faster the more damaged you are after battle (Anywhere from 1-5 TP depeding on, at best full HP, to at worst less than 25% TP), and using Escape adds two more TP loss.
9. Nitori is crap. By the time you're strong enough to actually get her... someone else is capable of doing everything she can, and far better. Also, it's... Encounter on 7F, event on 7F, encounter on 8F, event on 8F... Boss Rage on 9F. And, yes, characters you get in general are weaker than as bosses statistically... but several are still really powerful as allies.
I feel like I should pass on some notes: You'll want to use a couple characters if you want others.
*You can only get Kaguya if you've been using Mokou, Eirin, Reisen, and/or Sanae a lot (The more of em you use, the faster she'll be available), but you need to reach 16F first anyway
*It would appear you need to use Rumia, Youmu, Patchouli, and Chen a fair amount to get Yuyuko, and apparently she's required for Orin
*There's also Yuugi on 5F who may not show up at first, at the northwest corner; come back later to get her if she doesn't show up (It's based on battle count)
Anyway, Japanese wiki is at
http://www19.atwiki.jp/th_maze/ (Good luck running it through Google Translate. As a hint, " Sen Institute plantain flower bells Inaba ") ; there's maps and stuff (First three menus on left are for Main Game; second set are Plus Disk), if you get stumped/driven nuts (See F7...)