Does this word break one of the Irish spelling rules? Strong with strong, slender with slender?
No — ae is an uncommon digraph in Irish, and it’s always broad.
I run into some now and then. ("Anseo" and "aerfort" come to mind.) Just goes to show that grammar is just a set of rules-of-thumb that attempts to describe a living, evolving thing.
Since there is no t-prothesis, is this word feminine?
I think it's probably more appropriate to say that there is no t-prefix because "aeráid" is feminine, but yes, you can use the lack of a t-prefix to arrive at the conclusion that "aeráid" is feminine.
I see aeráid with a mental picture of barrage balloons.