Yeah I should possibly not go that in depth right away.
Sometimes game controllers have turbo built in. This is usually like I said with the device sending rapid pulses but built into the board itself. Obviously you can't buy a 3ds with such a thing so you would have to make it if you wanted to go that way. The same things people use to make those external controller inputs and manually remap things with wires being the main plan of attack there.
It is not that bad as most programmable chip things (arduino, teensy family stuff...) have blinking light of various speeds as their test/my first program thing for it and this is basically that, the my second program being how to make the light blinking speed change in response to the press of a button. The fine tuned macro stuff is not that much worse either but that is not what you asked for.
If you can solder then you can do this.
PCs since... maybe the early 90s have had it such that they run an OS which handles most things for the computer, and code runs on top of that. This is a relatively new concept for Nintendo handhelds though and everything before... maybe the DSi had the game itself handle essentially everything as far as managing hardware. The 3ds shook this up and had its OS run all the time and handle figuring out what the controls were doing and then passing that off to the game. This is why there were custom firmwares, plugins and such that allowed you to easily remap controls to whatever you like. The very same thing that allows you to do that would also with a tiny bit of tweaking allow a rapid fire mod to be made. I am not so familiar with the specifics of these mods though beyond knowing how they work in the broad sense so can't offer too much more there. Much like the game specific stuff I cover shortly you are likely going to have to get your hands somewhat dirty with assembly here.
Should probably cover debouncing as it is term that not everybody knows. Switches are mechanical devices. Go down to the millisecond level and a switch turning off might still see some elastic movement in the circuit that makes it appear on, and then off the next millisecond before going back on (it is called switch bounce hence debouncing)... this can make games do strange things if they read the state all the time to do different things on the same press so they will typically copy the state at one point and have everything operate off that for the next frame or so and grab a state next frame and carry on doing that.
The older methods though still work. You can still drill down into a game and figure out what it is reading for controls, and insert your own code to virtually do rapid fire. Said debounced section is usually just a point in normal memory the game had available. The simple control remap would say if bit 9 is high then set bit 8 high and set 9 low, if 8 is high then set 9 high and set 8 low. Now you have one button doing another thing in the game. Turbo fire is not much more complicated than that. You just set it to go on and off according to a pattern, possibly with a counter as frame to frame on and off is a bit much for most purposes. The combo to use it is much the same -- rather than just say bit 9 is high then rapid fire you say if 9 and 11 are high then do rapid fire. Enable/disable is similar -- you would wait for a certain combo of buttons to be pressed, set something that says to your mod that turbo fire is enabled (if you already have a counter it is nothing drastic) and to do turbo fire for a single button while it is enabled.
In any case such a game level mod is fairly in depth and I don't see a way you are going to do it without getting your hands dirty with some assembly. As it is fairly basic though it would make a nice introduction to it all project if it is something you really want.
Just to note there are a couple of other ways old school controller remapping worked. Mostly you change what the game looks for, and if the game itself has some internal control configs (be it complete, partially blocked or just a few premade schemes) then that by default opens up options for the would be control remapper.
You mentioned moon jump/infinite jump and some people assume it is related to controls. I tried to quickly cover how such things typically work, and gave another method of attack there which might work if the game works in a certain way.
I should probably also note that while turbo fire is a well known term (I don't know when it first appeared but I had a turbo fire controller for my commodore 64, and the NES advantage is an example of an official controller with such functionality) then turbo mode around here tends to mean like what happens when you press space bar in some emulators and everything speeds up to 600% normal speed. Such a thing is very hard to do in hardware, slow motion though is a bit easier.