with your training points, is it only those few skills that can be trained up? no way to raise spell points, etc..?

close, long range, critical (lockpick?). im guessing no trainers to raise up spell points, etc.

Yes, only skills can be raised with training points. Close range combat and long range combat can be raised on most islands, but only on Nakiridaani you can raise them for Mellthas. Critical hit can be raised on Maini and lock picking can be raised on Umajo.
HP and MP automatically raise when you level up.
Attack and defense are entirely equipment based.
2 attributes can be raised once on Nakiridaani for the whole party. Other then that you can raise them by standing on blue flowers on the Island of Peace for a few ingame hours.
The power of the spells is raised by casting them a few times.

Luckily:
1) casting characters have both magic stats nearly maxed up
2) there are plenty artifacts that boost these stats even more (I love left-hand wand, that can be found in Guildmasters secret room, that boosts also max Spell points and Magical stats. Very neat!)
3) speels go stronger as you use them. So if you want Khunag's Thunder Strom or SIra's Frost Avalanche deal max damage, just use the spells on random encounters for a while and there you go, TS dealing 40 DMG and Frost Avalanche 27 DMG (applies for every spell)