Generac transfer switch questions

Purchased home that has a Generac Guardian 16kw propane powered standby generator with a generac transfer switch.  I have a couple of questions hope somebody can answer. 
 
1. Assume utility power is off.  Transfer switch worked and generator is running.  Everything works fine.  If I put generator off in order the conserve fuel and the utility power comes back on, will transfer switch switch back to utility power?  
 
2.  Different question.  If utility power is off, transfer switched work and generator is running.   Fuel runs out and generator stops.  What happens when utility power comes back on?   What potential mechanical/damage issues are there with generator running out of fuel?  
 
Thank you.