this game makes me feel old

[Renmiri]

Should I have concentrated my magickers into one particular magick type or should I have kept them general?

White for healing. Arcane and Green Magick are more useful than the rest IMHO. But as Endless said, physical attacks work best in this game.

Should I even bother with Technicks?

YES!!!! Steal, Charge & Telekinesis of course but also:
- First Aid - gives you 1/4 HP back for free, no MP required, as fast as an item.
- 1,000 Needles - consistently hit 1,000 there are no monsters immune to it (iirc)
- Bonecrusher - Another one few monsters are immune, and takes their HP down a lot
- Revive - 100 % MP and MP for the character you revive. You still waste a Phoenix down on the character who cast it, but having full health and MP for "free" can't be beat

And how many weapons do you usually specialize in?

Axes did all I needed.

Do all characters need to be the same level or can I get away with only using three the entire game?

Second party should be at least strong enough to revive the main party (3 turns)

Is a conventional "class restriction" a la FFT better or worse for this game?

Unless you are a purist, don't bother