Things I want to do with my version of FFVI.

Hello. You've quite the ambition.

2) Break damage limit was accomplished by Giangurgolo and he released a patch called 32000 Overkill. It is so named because damage still has to fit in 15 bits (32768) as the top bit signifies healing.

3) An FFVII-like limit system would require rather major code rewrites. However, if you're proficient with 65816 assembly and are determined you could do it.

1) The behavior of Runic isn't a bug - it's supposed to shut down all magic. Rewriting code to only trigger Runic on enemy spells is feasible; in fact, I've done it. It makes Runic incredibly overpowered and a headache to balance around, so I scrapped it.

2) Removing enemies from the collapsing house is as simple as editing those maps with a map editor and unchecking "random encounters". Changing the time limit would be done via event editing - admittedly something I know little about, but very doable.

3) Changing H-Bomb is an interesting project because it requires many different methods. Changing the spell name, power, effects, animation, etc. is as simple as editing the spell in FF3usME. Making new animations is difficult because it requires writing new animation scripts, but cobbling together existing animations and palettes into something different-looking is rather simple.
Changing the Slot reels requires decompressing some graphics and editing them with YY-CHR. Again, doable.

4) Changing Celes' natural magic is easily done with FF3usME. Learning spells via event doesn't happen in the original game, but I believe there exists some unused event code for it. I might remember incorrectly, in which case it would require writing new event code in addition to editing event scripts.

5) Again, simple map and/or event editing.

2) (What's with this Star Wars-esque numbering?) Adding Summon can be done with FF3usME and there are patches that fixes the Summon command to work properly. It lets you summon the equipped Esper as many times as you like, that's it. Anything beyond that requires major code rewrites.

3) Adding new spells is possible thanks to B-Run's MMMagic hack. It allows 10 new spells to be added to each character's spell list. There are some unused/dummied spells in the game, you can edit these new spells with FF3usME and assign them to characters with B-Run's patch. However, for something like Valor (Aura is a spell from FFVIII), you would need to hack some code.

4) I'm not sure you can start playing a song from the middle. You could edit a song and cut out some parts, and replace the battle music with that. Editing FFVI's music is pretty complicated and there are no editors for this. You have to learn the format and do it all by hand.

In all, all these changes requires A LOT of different skills. If you don't know 65816 assembly programming, or the SPC music format, or general romhacking knowledge, be prepared to spend a year or two learning the ropes.