All the house rules during teen years were all based on getting the kids to be independent. This is the time they became responsible for their own laundry, shopping, a turn in the cooking rotation, dealing with their own dr and dentist appts., budgeting etc...
Yes, they had to let me know where they were, just like I let them know where I was.
As far as the problems you mentioned (with friends, lying, mouthy) mouthy didn't happen much, but when it did happen I just reminded them that I talked to them with respect and expected the same back. That doesn't mean that their weren't disagreements - what helped on that is when our son would be angry about something I would just tell him to put it in writing. He was allowed to say whatever he wanted, using whatever language he wanted as long as it was in writing. Many times he'd write something down, and that was enough venting that he just threw the paper away. The times he did give me the paper I was able to get to the heart of the problem, without the stress of an angry delivery. I would reply back the same way - it took a lot of the extra emotions out of the situation and worked really, really, well. Once we made that rule, as soon as a conversation started to become heated one of us would just state "put it in writing" and we knew that there would be no more verbal conversation about the issue until it was resolved.
The friends problem - you may not like their friends, but when it comes down to it - they get to pick their friends, you don't. It's hard to step back on this one but you don't have a choice. To fight it would make the friend bond stronger not weaker. Such is life.
The lying would drive me crazy. You have to find out the why of the lie (are they afraid of disappointing you? Are you too tight on the rules? Or is it just general lying for no reason?) you have to find out the why and work on a compromise from that angle.
Good luck