There is absolutely nothing in the Bible to suggest that angels have a different language (perhaps they communicate telepathically amongst each other).
Every recorded instance in the Bible shows them using human language (Hebrew or Aramaic).
You left out Greek.
The problem with your line of reasoning is that in every incidence in scripture of angels communicating to humans, they were communicating to humans. Humans understand human languages, so they spoke human languages. As for angelic languages.... we know little about that.
Scripture says nothing about angels communicating with each other telepathically. You do not have a problem with that idea. But scripture suggests the idea of tongues of angels, and you have a problem with that.
Those who make this point all seem to be reactionary...trying to take a firm stance against the existence of tongues of angels to form some theological position on speaking in tongues. This is not proper exegesis.
So Paul was simply speaking in a hyperbole -- just to make the point that even something that bizarre would be meaningless without charity (agape).
The rest of the arguments, most of them at least, are undeniably possible extremes. It is possible to give all away and to give one's body to be burned. As for having all faith to remove mountains, Greek can be looser about the word 'all', and it is possible to have faith to remove mountains. If Christ meant His words about that literally, then it is literally possible to move mountains and if it were figurative then it is possible to figuratively move mountains.
Paul suggests the possibility of tongues of angels, so we should be open to that. The idea that speaking in tongues IS tongues of angels is a weird idea held to be a few Charismatics I encountered, but not a standard Pentecostal position or historical Pentecostal position. Pentecostals would make some room for the idea that an individual tongue might be tongues of angels because Paul suggested it. Or that seems fairly typical on the occasions I have discussed it with Pentecostals.

