Yes - you would receive the call the same as if you were home. BTW, my only personal experience is with AT&T as the carrier, but I understand Verizon has the same features.
Yes - exactly the same. Similarly, if you get junk calls (like most of us), they'll come through too. What we do is put our phones in "Do Not Disturb" mode so they don't wake us up (I assume Android phones have something like that). When I get up in the middle of the night to go to the bathroom, I check to see if anyone important called.