Unless your ISP can't give your router an IP because they ran out
No, they'll either reuse their existing floating IP addresses if like most people, you don't have a fixed IP.
If you have a fixed IP, they'll probably assign your router an IPv6 address - dealing with them is their concern. Pretty much all modern routers can deal with IPv6. Your router will continue giving out IPv4 addresses on its internal network.
Again, the only people who need to worry are these who deal with multiple networks and WANs over IPv6.
If all you do is remote login to your home or work computer (which is more advanced than 99% of the population) some minor tweaking might be needed.