A few things:
1) How old is the keyboard? Different age M122s register function key presses in different ways. I believe all newer boards (meant for AS/400 terminal emulation) register the higher F keys as (shift + lower F key). For example, F13 = Shift + F1. I'm not sure this can be changed. Older boards (originally meant for tried and true dumb terminals) should have unique scan codes for all function keys. This could maybe explain weirdness with the extra function keys?
2) What kind of converter are you using, if any? No converter + older board will show odd behavior, if it works at all. This is because Terminal boards use a different, "sort of" compatible scan set than most modern boards. Soarer's Converter you full remapping capability, plus the ability to create function keys, lock keys, and macros. You can either mod the keyboard with a chip (also converts to USB) or buy them as a dongle on ebay. They're a tad pricey, especially the plug and play model.
Finally, there's the chance that the traces on your board are damaged. Only way to know this would be to open up the board, and I don't recommend it for an M-122. Replacements are fairly cheap on ebay (I've seen as low as $20 on some days.) If you're careful and play your cards right, these boards can be had for less than the price of a converter, so patiently waiting and buying a new one would honestly be the cheapest way to tell if your board is busted!
That's all I've got for you. Good luck!