I believe if you set WMC as a DVR, it should wake to record. At least, that's what I've read about it. I'm pretty sure it is necessary to have it in sleep mode versus hibernate since it can resume faster to record.
I would think pressing any button on the remote should wake it, but you should test it yourself to see if it does, and if not, try to troubleshoot USB wake.
And yes, Windows will sleep when not in use, if you power options are set so when you're playing media, it doesn't sleep. But if you're not doing anything, after a set time, Windows will sleep/hibernate.
Hope that helps!