In what kind of circuit does current flow?
1) YES - The current will flow in the loop and it's value will be decided by the voltage of your power supply and the resistance of the path.

2)YES - The electrons will flow from negatively charged body to the positively charge body until both bodies are at same potential. Once that happens, no further electron flow will take place and hence no current will be flowing. This case is sometimes referred to as a transient current.

3) NO - Current won't flow because both batteries are uncharged objects. Also, net potential difference the bodies of those batteries is zero.