I can't help you with point 1, as I agree that this should be impossible. What you propose in (2), however, (accepting only pseudo-legal moves) would make it impossible to use WinBoard as a GUI for unsupported variants by switching legality testing off.
It could very well be that Na8xg4=K capturing an own Pawn is a legal move in some variant. Promotion to opposite color is too exotic even for my taste, but I did consider allowing promotion of any piece on any move, and I might still do it. (But you could not enter such mover with the mouse then, and in XBoard you cannot enter moves by typing, so I shelved the idea.)
I currently also do not allow capture of own pieces through the GUI interface. This would interfere very much with the current way of entering moves by mouse, where a new click on another piece selects it in stead of the one you selected before, and people really value that. Even abandoning this for Rook-after-King clicks for the purpose of entering FRC castling led to immediate complaints, so now I limit that to FRC and CRC. And even there it never means that you really want to capture the Rook. I might add a variant where capturing own pieces is legal, though, and then only in that variant the mouse behavior would have to be changed. For now you would be abe to play such variants only by typing the fratricidal captures in WinBoard, where they accidentally worked even in 4.2.7, and I saw no reason to change that.
Apart from the above weirdness, it does not strike me as odd at all to have WinBoard accept Na8xg6 or Na8-g6. There can be variants with pieces that move like that, and where a Knight would be the natural representation. There are all kinds of variants with augmented Knights. The sole purpose of being able to switch legality testing off is to play such variants. Note that WinBoard has always had this design philosophy: in WinBoard 4.2.7 you could only play Shatranj (w28) on ICC by switching legality testing off, because otherwise moves like Bf1-d3 would be refused if e2 was occupied. (And of course many moves would be refused because WinBoard would think you are in check by the Queen, not knowing that the Queen was just a Ferz in Shatranj.)
Fairy-Max supports castling with corner pieces of any type. This is needed for Chess with Different Armies, where to most one side has Rooks, and the other side has something else, while both sides should be able to castle. E.g. the army of the Color-bound Clobberers has a corner piece that moves like a Bishop or makes a (2,0) jump in any direction. A Bishop would be a much more natural representation for that than a Rook, and an Archbishop would be even better. But they must be able to castle. If WinBoard could not handle that, it would not be a suitable GUI for Fairy-Max.
If people enter strange moves, with legality testing off, they should be neither surprised nor confused when strange things happen: the result of such moves is undefined.

Only with legality testing on, there is the defined response of the illegal-move popup, (or a forfeit when you are an engine). With legality testing off, only moves (pseudo-)legal in the current variant have a defined respose (namely performing that move). Users that find that confusing, should not switch legality testing off!