Will the shuttle drop me off at my departure terminal B at Lax

Yes

Is there any shuttle service between the LAX airport and this rent-a-car location?

Yes. You just tell them your airlines

Yes, let them know when you get on the shuttle. Stay towards the front of the shuttle if you can.

I dont know i would assume so , i know u can call there 1888 number on there web site and they would be able to anwser