Have you not tried looking through one of the very nice commented disassemblies?https://gist.github.com/1wErt3r/4048722
Unlike most games where you are very much on your own (or whatever you can glean from game genie guides, the wiki here and such like) then that is pretty much something you can follow along with as a lay person. Most of what you want there is also stopping things from happening (the last one might take some effort and understanding) so you don't even have to figure much out as much as NOP (short for no operation, basically makes the device carry on as it was and go to the next instruction without changing anything) or jump past the code you don't want/to the end result you want (there are some around here that upon coming to a fork in the road will be able to tell you all about road building, and that allows them to do some terribly impressive things, but most of the time you will only care about being able to pick the direction).
Worst that happens with that is some of the phrases are not necessarily what the manual, community or general phrasing might use and you get to try some others, or scan around for something else that uses it.
If you want to spend 5 minutes learning how to figure out what instructions are being executed at a given time in the game by using a debugging emulator then even better still (the game might be playing the "you have an invincibility star" song but shortly after that it will probably be figuring out something with the flashing graphical routine and you can then follow along with the assembly in text form). Spend a few hours learning how to set breakpoints and so much the better.
"I'm pretty good at using utilities."
So is everybody, give or take 5 minutes to get use to the level design flow for any random game. The trouble comes in that unless someone has thought to make the hacks you want and encoded them in then you are only going to be able to edit within the scope of the editor. You then get to get your hands dirty.
On "middle of the screen" then I should probably link a favourite documenthttps://docs.google.com/document/d/1iNSQIyNpVGHeak6isbP6AHdHD50gs8MNXF1GCf08efg/pub?embedded=true
For some general "how I would approach it"
How do I remove flashing effect from fire flower and super star?
Flashing is something that is done. Figure out what changes and hone in on that. I would use a debugger but you might find it in the disassembly too.
How do I disable Bowser's front hitbox?
Hitboxes can sometimes be software defined in file formats (many fighting games are this) but for a game like this it is probably code. I would instead look at the fireball code.
How can I make it so the screen scrolls only if Mario is in the middle of the screen?
Scrolling is a thing that is done, but it probably has a condition that it only occurs at a certain screen location, and even then for bosses and end of level is likely fixed. Commented disassembly probably has a nice thing. You will probably want to be changing numbers here rather than blanking instructions and skipping things.
How do I make it so if Fire Mario takes damage, he only goes back to Big Mario and not back to Small Mario?
Some have done this before if memory serves. Anyway mario has different state values. A cheat probably even exists to be always a certain size. Find this memory location and what changes it. Alternative what happens when hit/collision/hit hazard? Something will change from fire mode to small, however you would want to set it to just big mario.
How can I make the title screen just on a blank background with no demo?
As you will probably not be able to blank out data without breaking the rest of the game you get to attack the code. Being one of the first things in the game then demo mode is fairly well covered in the commented disassembly.
How do I stop the bottom pixels on the UI from glitching when the screen scrolls?
I recall some looking at this before. Still this is an actual thing that might take some knowledge and understanding of the hardware, though you might get lucky and it is one of the easier programming errors to sort https://textexpander.com/blog/the-7-most-common-types-of-errors-in-programming-and-how-to-avoid-them/