• Psionics
• "Saving Throws"

As a general note, when it doubt, use a GURPS rule. Planescape as a whole is much more a setting than a collection of rules. If you're on fire, find GURPS rules for fire rather than trying to convert the AD&D rules.

Psionics

If you use Psionics, use the GURPS system from the Basic Set. It is entirely different in nature from AD&D Psionics, but meshes far better with the rest of the GURPS rules system. This means that psionic characters and creatures will have substantially different powers. However, the important thing about (for example) a Mind Flayer is that it is a fearesome master of psionic powers, not that it has such and such specific abilities. Yes, the game will be somewhat different, but then again a different game was part of the whole point. The important qualities (in this case, that Mind Flayers are psionic and to be feared) remain, and you still have a playable game.

"Saving Throws"

Resisting spells is covered by GURPS Magic. For other cases where the Planescape books say a character must "save vs xx" or suffer some terrible fate, replace it with a roll against an appropriate attiribute, frequently at a penalty. This will usually be rolled against HT or Will (but in all cases is up to the judgement of the GM). Sometimes, e.g. when a fiend is attempting to use a special ability on a character, it is more apropriate replace the "saving throw" with a Contest of Will (or another attribute); in this example, it might be a Contest of Will between the character and the fiend. (Bear in mind that many fiends should have very strong will!)