I'm pretty sure that the IP address expires along with the DHCP lease or when the cable modem is disconnected.
for the most part, yes. Funny thing is, I have to keep my cable modem off for an hour or better to get it to give me a new IP..I have had the same IP for months now. The only time my IP has changed since I have had RR, is when RR reconfigured the line I am on and gave us all new subnet addresses.