I'm not an expert, but that never stopped me from giving my opinion.
If the first rejection included suggested revisions that made your book stronger, I think a thank you is in order. Other than that, I don't think it necessary. You would just be adding to the agent's email load.
I don't see why you shouldn't query the other agent. If they wanted a rejection from one to be considered a rejection by both, they could have said so. They didn't.
Sorry about the R.
If the first rejection included suggested revisions that made your book stronger, I think a thank you is in order. Other than that, I don't think it necessary. You would just be adding to the agent's email load.
I don't see why you shouldn't query the other agent. If they wanted a rejection from one to be considered a rejection by both, they could have said so. They didn't.
Sorry about the R.