Spell-wise these are the wrinkles I see:
Dimension Door & Teleport - these use hyperspace as it would be used by starships in the long-ago golden age. So, fine we have one sort-of other dimension used for travel purposes - you still can't go there.
Commune & Contact Higher Plane - these are pretty simple. Commune lets a cleric talk to a higher power, all of which live on this plane. Contact Higher Plane refers to consulting with another being so it should work the same way - call it Contact Higher Being and don't worry about what plane they are on.
Summon Elemental - In this world, elementals live in their element, not off on some other plane full of it. So M-U's summon them from the nearest concentration of earth or fire or air or whatever.
Invisible Stalker - these are specifically mentioned as coming from another plane but they are invisible and do not appear to have any society or culture or equipment of their own. So instead, even if it is believed that they come from another plane, I'm going with a different theory. In this game Stalkers are a localized coalescence of nanites bound together and given a purpose by a magic-user casting this spell. they have no individual personality and when the spell ends they disperse into the air as if they never existed. That makes this spell fairly important as it means that sometime somewhere at least one magic-user figured out how to access and control the nanite cloud in at least one specific way. Alas, the knowledge must have died with him...
If we go to companion level games (and we may) we start bumping into the whole "Immortal" thing that was part of the teal and black sets with spells like Gate and some of the monsters that show up there. I will deal with those when they come up but I will keep the "no other planes" rule in force. Maybe gate opens up a gate to a distant continent, maybe it's a remnant of a communications protocol and opens up to an orbital facility or the moon where all kinds of weird things could live! The more oddball monsters from the various planes could be from the "Plains of Nightmare" rather than the "Plane of Nightmare" and be tied to an actual physical location.
Raise Dead spells and Reincarnation spells are comparatively easy - there is nothing that fantasy nanites cannot do, including respark a dead body.