Oh dear, you really sound like the type that put dodgy wiring in cars. Seen it so many times. This is car electrics 101, just run a cable for the purpose.Well, if a manufacturer advertises their sub as a 250W unit it probably means that the sub amp can deliver that power for a few milliseconds only even 120W of constant use would be one hell of a noise.... So I would not worry about that, if you exceed the power delivered by the outlet it'll blow a fuse.
No no no, not another oneThis... 250W would be instantaneous drain at high load and you wouldn't sustain that for long. As you noted, 120W would be a lot of low frequency noise sustained as well. More than likely you would never see more than 60W with occasional peaks to 100. This is what capacitors were made for.
And by the way a sub isn't supposed to make a lot of noise, if you can hear it you've done it all wrong