Since the modem is handling DHCP, there will be a field somewhere showing the range of IP addresses it is managing: for example, x.x.x.2 through x.x.x.64. You simply make sure you assign your fixed IP addresses outside that range. In the above example, 65 and above are freely available to you.
In other words, look at what the router is managing, and you simply assign the rest.
Re the IP camera, look again in a few days and see if it sorted itself out after the lease expires.