Can these sentences mean the same thing?
They can but they don't necessarily mean the same thing. If you are staying at Charlie's place, then you can correctly say you are staying with Charlie. You could also be staying at Charlie's place when Charlie isn't there, and then, you would not be staying with Charlie. If you are out somewhere with a group of people that is splitting up and you say you are staying with Charlie, you are not staying at Charlie's place.
No. A.) you could be staying at a Hotel with Charlie. B.) you are staying in Charlie's Home, but Charlie could be out of town. Yes. In the most General of common usage, yes they *could* be the same. But, I believe it would leave the listener confused.
Not necessarily. You could be staying, with Charlie anywhere, at Bob's place, at a motel, in a tent.. Or, you could be staying at Charlie's place while he is out of town.
Location and who you're with are orthogonal. One has nothing to do with the other. For example, you can be with Charlie but not at his place, and you can also be at Charlie's place when Charlie isn't present.
They can, but not necessarily. You could be staying with Charlie at a hotel, in a tent, at his Family's house, at a Friends house, etc. And... You are staying at Charlies house, while he is away.
You could be at Charlie's place with Nancy
With charlie can be anywhere but physucally together At his place is inly at his place he could be gone out and you are still there
With the right context they could but as they are - no.
Yes, they can mean the same thing.
No. A emphasizes you are physically with Charlie whereas B emphasizes you are staying at Charlie's home, but does not indicate whether Charlie is there or away.
They CAN. But a context is necessary for deciding whether they DO.
Yes. Both can and usually do mean the same thing.