IDA first then.
There are many families of processor. Most PCs you will likely ever have used will be in the x86 family.
You say you are familiar with the GBA. That would be the ARM7TDMI. The DS also uses an ARM7 but the main processor it uses for commercial games is an ARM9. It gets a bit more confusing if you want to consider the name/version of the ARM instruction set each processor runs but we will skip that for now.
NES is 6502.
Master system is Z80, and the GB/GBC kind of is as well.
Megadrive/genesis is 68000 aka 68K, though for the sound system it also has a Z80 which can do code in its own right.
Many consoles have used some flavour of powerpc over the years. Older apple stuff also went in for them.
Rounding it out though we have the MIPS family, of which the PS1 is an example of users of it.
All these families, and indeed revisions within them, have separate ways of interpreting 1s and 0s to make instructions. This means each disassembler will have to be coded with it in mind. IDA has many of these already in there, and some excellent means of defining more and the option to handle quirks and memory layouts for specific systems. The free version however is limited to X86 it seems, which is fine as prior to this explosion of mobile phones and tablets it was the main thing anybody would have cared about. No MIPS in sight and I don't know if you can even add it.
You mentioned ruining the ROM. This should be a non issue. You should be working from a backup of it, and back up work you are doing at stages so you can revert back to an older version. I know you were probably trying to say you can edit this with the least unexpected fallout but I am going to highly discourage such thinking.
On the face of it then spectator mode might seem like something you can "just" (just is a swear word for most of computing as it usually involves an assumption on how much work needs to be done and said assumption is usually rather off the mark) add to, or if the game is coded in a way that it could well be then simply "unlock" the option to have players*
*it could well be that something as simple as the cheats for forcing a character could well have the game cede control in spectator mode to a player, and it gets more likely if there are not weird and wonderful abilities given in spectator modes as far as cameras. If however it is a whole new mode (the PS1 having hundreds of megs of space thanks to the whole CD things means it is able to store a few hundred KB of standalone program that is spectator mode if it wanted to) then that gets more tricky. Adding controls in is not a monstrous task but it is similarly not something I would chuck someone new to all this into and expect them to do well at it, especially not when other things are likely easier -- cheats are simple (more on them in a minute), and fiddling with a random generator such that it selects a number slightly outside its normal parameters is also nothing drastic (don't know what it will be here but you are either fiddling with something it already does, or telling it to do nothing at a point when it would have done something. NOP is a good term you will want to read up on for the latter).
On abilities then if it is a thing you select and not inherent to the selection of racer or something then such a selection will have to be noted in memory somewhere. If it is not bundled with the character selection itself (given the distances apart each of those cheats are for each character I would definitely have a look -- if said memory locations were just to note the individual character selection then that is a lot of wasted memory, memory most PS1 coders would not waste like that) then chances are it will be with another big list of such things. Either way as you can control abilities selected then you should be able to find easily enough with a cheat search if you note what you are doing for each race and search accordingly, though first I would take the memory addresses those cheats have and look there to see if the abilities are there as well.
Cheats then. These are pretty similar for all systems. They work by having a menu in the emulator, or in some occasions a program like emuhaste, artmoney or such attached to it. Here you will start the cheat search. Then in the game do something. Depending upon what was done you do another search. For instance if you want infinite potions you would buy 99 of the things, start the search, chug one, do a search for things less than they were at the first search, chug one, do a search... eventually things will narrow down such that you can try things manually or just have one left. You might try searching for specific numbers as well to narrow it down even quicker.
For abilities then it would take longer than opening a menu to chug a potion but it is still the same plan.
Things greater than, things less than, things that changed, things that remained the same, things within a range and things outside a range are the default things pretty much every emulator/cheat search will have. Some will have some more exotic options.https://web.archive.org/web/20080309104350/http://etk.scener.org/?op=tutorial
is a guide to making cheats, it is aimed at the GBA but again it will be the same for just about everything out there. It will also cover the basics of anti cheat methods that some developers employ, or code in such a way that they effectively employ.