Yes....you can give ur mac "self-assigned ip addresses", but then you must turn off DHCP in the router config or it is going to conflict, especially if another device has already been assigned the static ip you have given to your mac. You either have DHCP "on" on both the mac and the router, or it off on both, you can't have it both ways.
Yes you can. I have DHCP enabled on my router and I have a static IP assigned to my Mac. To avoid conflicts, you just use static IPs outside the range of your DHCP server. For example, configure your router to use 192.168.1.1-192.168.1.100 for DHCP, and then you can use 192.168.1.101-192.168.1.254 for your static IPs. No conflicts, works great.