There are UI scripts for using things like Nuke or Recall, however these don't cover every single ability usable in-game. Are there particular methods to making templars specifically cast storm in one specific spot? From what I understand, as long as the templar has one target to attack, it's not within it's own range, and it has enough energy, it will use storm on the specific target.

Basically, I wanted to know if any of you have had any problems in this area and if there are any particular guidelines or tricks to doing this.

In the wiki for Getting Computers to Use Spells, or Spells(Protoss) for you, it tells you the only way to get it to work, and not even that is perfect, there is no actual AI(AI = Artificial Intelligence, UI = User Interface) script that you can use to MAKE them cast Psionic Storm.

Alright, here's a good little trick to perform. Is it possible to make a unit(Firebat)not attack any units around it, without changing alliances and still be able to move the firebat around normally or with using the Order trigger? Assuming that the firebat is actually being attacked by multiple vincible targets, uncloaked and actually damageable.

The only method I can think of is to have a hypertrigger Move Order that will have him stuck to a specific moving location.

I realize I'm going off-topic on my own thread, but I don't want to start too many threads now do I?

Well, I can't think of any way to make it, without alliances, so that the units attacking it would be able to attack it properly, all the ways I know of would either cause them to miss continually, or keep losing their target. Do you want one of those?

You pretty much answered the question yourself. Move order and hypers is all you can do with these requirements.
Maybe you should replace the firebat with a non-combat unit like the civilian.

About abilities of units, you can trick the computer in using them, which might be a little tricky sometimes (wiki tells you how) but there's no way to order a unit to cast a spell (except those 3 that have AIs for it).