Can someone drop off a animals they rescued off the streets?

Yep

Yes you can

Yes , you can bring in strays . I don't know what process there is, but it is a rescue shelter and you should have no problem leaving the dog. They will try to find a home for him or her. I would explain to them that you can not keep the dog and hope they find it a good home

Yes they can but their is a process

Yes

of course YES