I tried the first one (FAJHMFIJJS) on Lemmings on PC/Dos and it gives:
Code for level 1
Rating Bogus
Then, at the right part of the screen on the main menu where we can select the rating, everything is snow-colored (if you understand what I mean) and if you press the up or down arrow keys, a lot of other colored-snow appeared. I even guess that I saw the main menu inside! But if you begin by pressing F1, then it shows:
Insert Disk Into Drive
Then Press Any Key
For the other codes: Incorrect codes.
As I can see, this code is like reserved for Two Player levels. But there's no 2-Player levels on PC.
For me, on PC/DOS, I got all three codes to give results.
The first gave Rating (blank), but the letters "ou" appeared in the top left of the screen. (I'm guessing that the first character in the Rating name was one that sent the cursor back to the top left of the screen, where it printed a Y off the screen.)
The second gave Rating "r time", and the third gave Rating " is up".
The strings spell out "(Y)our time is up". All three did the "Insert disk" type message when you try to play, though.
For the second and third codes (but not the first, which you can't change), you can keep cycling through the difficulty ratings, getting different garbage graphics each time. Sometimes you can even make out "Tricky", "Taxing", and "Mayhem", although they may be in a bluish color. If you go far enough, you get back to the regular difficulty levels, and can't go back down to the garbage.
Ahribar, it seems there is a good possibility for a connection. FAJHMFIJJS looks like a code that you could get for beating Mayhem 30 (but of course you shouldn't get the code, the game should end). The second to last letter is a big clue to the position of the code (look at any list of codes and you'll see what I mean). For the latest Mayhem levels, this is J. The latter two codes have L and N as the second to last letter, and this makes sense assuming the two-player levels are all listed after the one-player levels in those versions. I'm not sure how the two-player levels work in those versions that have them, but could it be possible that there exist some codes in the PC version that reference the two-player levels but just don't point to anything? You'd probably get the same garbage as the other codes give you, but it's interesting anyway.
Edit: Ok, the level # is determined by the next to last and third to last letters, always! This is also consistent with FAJHMFIJJS being a code for the level right after Mayhem 30.
An interesting note: I tried typing in a random code with "KJ" as the third to last and next to last letters. I got the message "Incorrect Code". However, when I tried starting a level, I got the "Insert disk" message! When I typed in a bunch of random codes with "BC" as the third to last and next to last letters (would be a code for Fun 1), I didn't get this error. Weird.
Maybe this is when a semi-valid code appears and the game has to validate it, but can't, because the levels don't exist... or something like that. (It only happens sometimes.)