No, that is true. Thankfully in most situations if you can licence via a rights agency they will handle the international aspect with other agencies on your behalf. And if you negotiate with the artist's management they can also do this - providing they can reach agreement with their publishers and agencies that they have existing agreements with, which is not guaranteed! (A condition of working with some of them is that they alone get to issue licences, to keep things simple.)

No, that is true. Thankfully in most situations if you can licence via a rights agency they will handle the international aspect with other agencies on your behalf.

Yup. That's how it works with film audio as well.