i am finally told that it is not possible to print from the iMac to a printer that is wired to a PC that is itself not wireless even although the PC is connected to a wireless modem router. Apparently, in this case, the printer should be connected to the router, but no USB on the router!
Whoever told you that, told you a load of nonsense. Printer sharing is perfectly possible between Macs and PCs, no matter whether the printer is connected to the PC via USB or it is connected via the router.
There's just something wrong somewhere in your case, that's all (possibly something related to port setup, or 'print services for Unix' not being enabled on the PC).
But if you've managed to sort it another way, then fine.