A Honda gx390 13 hp is a 13hp... however a new style (after around 2010 - 2011) is only called a gx390 because of the engine cc, they dropped the 13hp because of euro emissions etc and had to restric the fuel consumption and emmisions to comply with these rules, in doing this the gx390 has a maximum output of 11.7 HP.... hope this help??
So in short a pre 2010 will be 13hp output (just look at the recoil aswell to tell) and a newer GX390 will will be 11.7HP
But BOTH will run a ws202 adequately, (even an old 11HP will run one, ive had them)
As regaurds to suction through one port on a ws202, the suction power is determin by the rpm... which is as you know 1450, the port is 1/2" and can only physically suck 18 or 19lpm through a 1/2 port at that rpm... (power shouldn't even come into it because a 5 hp engine will still turn the pump at 1450.... it just wont put it through a nozzle at the end.
I had a jetmac machine with a 202 on it the other month, when running the machine that came to me with only one port (as jetmac sends them out, which he shouldn't do, and neither should any other dealer whos worth their salt) I found that it would only go up to about 190 bar when turned up, I could also feel the restriction on the gun (the same feeling you get with a small air leak or a squashed suction pipe). I then, before even looking into seals and pistons, put another feed on the other inlet, fired the machine up to try again and instantly was up to full pressure at 200 bar, a nice steady solid flow.
So yes, a 202 does need twin feeding, unless your gravity fed then that would be a different story as it has a positive force so is having water pushed into it rather than sucking it up and over a drum against gravity