Ew phantasy star 3. For the sake of some future forum reader I will probably go with the mana-spell convention than techniques, technique points and such.
That out of the way.
Yeah assembly is your future here if you want to start changing effects in a meaningful way in most games, at least those that don't have custom spells or percentage enchants in them.
Should be fairly easy to narrow it down though as far as getting a starting location. Normally we teach people what to do so as to make a true invincibility cheat but the same method works here. For the health thing we find something that damages the health of the character and set a breakpoint on the health. When the health goes down the game says hold up this is what did that and you work backwards from there. Here you would find what damages the tp (in game/universe term for mana for those not familiar with the series). If mana is able to be set that easily it might be a lookup table affair so instead you might try health of the enemy (probably not here though for obvious reasons) or some other effect you know the memory location of if it has one. Alternatively it should first read the mana to see if you have enough so rather than setting a break on write when it removes the mana afterwards (possibly, might do it before casting/immediately after a check) you could set a break on read for when it checks to see if you have enough to do the deed.
The simplest thing to do there once you have it is redirect it to another spell. Here you could find the effects for another spell (same technique as the above) and set a jump to that spell's location. Not much good but you could do something like make a "mage" character have a cheap spell or possibly a single target version of a more powerful thing for another character.
After this then you are limited to minor tweaks -- increased damage is probably going to be easy enough (can't remember offhand if the 68K has good shift instructions but you can then do 2x, 4x, 8x... stuff quite easily if it does).
Start wanting to make your own spells from scratch and time for some proper assembly. You might be able to mix and match some things from existing stuff, and it should not be massively complicated -- save for a bit of randomness generation ultimately you have a few variables as far as player HP, TP, enemy HP and whatever else to play with, if you choose to include any defences to techniques as part of this then that is on you.