Is it possible to tap a cell phone and listen to phone calls without having access to it?

Yes, with a wiretap order that requires probable cause, before the surveillance begins, unless the following circumstances exist.

What is the most insane conversation you have ever heard by your friends while eavesdropping?

The most insane conversation I have heard were not by friends, it was being in the sauna at the gym. Apparently the men's sauna is on the other side of the wall. It had to be a least three or more men talking about women have to pay to have sex with