Yes, the camera can obtain an IP address regardless of whether it is from a 3G/4G router or a wired router. Just keep in mind that such a router as asked does not have a private IP and therefore the external access is not possible without further ado, this just so tur info.
Motion detection yes, ceiling mount no.
It is intended for wall mounting, I have made something with a metal bracket to mount it on the ceiling.
However, Reolink offers a completely overpriced conversion kit for ceiling mounting.