Is it clear that the permanent dealing damage is the one being exiled?

Hmm, no, I can see that being very confusing.

Reads fine to me, but I am fairly steeped in Magicese.

Oh, interesting card. (And quite simple, despite needing some minor templating tweaks.)

I can't tell which the current wording means either. If I think about it, I can tell which meaning makes sense, but I can't guess from the structure of the sentence which permanent "it" refers to, although if Alex thinks its unambiguous int the rules, that's probably right.

If it said "to you or a permanent you control" it would be occasionally confusing but IMHO be clear, because "it" can't be "you or a permanent you control". But I'm sure a fairly minor tweak would make it clear.

I'm also not sure what happens if it deals damage to multiple permanents simultaneously: does none of the damage happen?

I didn't want you to be able to exile something that hits you, because that ups the power level. If necessary, I could make that change.

The way I understand it, the permanent is being exiled instead of dealing damage, so it doesn't deal damage to anything.

How about "The next time target permanent would deal damage to a creature or planeswalker you control, exile it instead." Damage to anything else is probably irrelevant, and I think the "or" makes the "it" a lot clearer without sacrificing much. But any number of similar tweaks would also be fine, I don't think you need to change the functionality unless you want to (that was just a suggestion, not particularly thought through).