Can I make a channels called let's say "Proxy", setup one ad unit of whatever size, then place that code on multiple sites?
you most certainly can - but it's not beneficial to do that really it helps to know where the clicks/impressions are coming from, and also helps advertisers target the space (if you have that switched on)
making full use of custom channels is really important - for your own sake more than anything. I don't know much about proxy sites - are they even allowed under the TOS? I'm not sure on that one, maybe someone else will be able to help!
Having channeled ads block is very important. I recommended you to do so, each new blog with new channel on different site. If you have 10 site, create 10 new channel and 10 new ads block. That will help you monitor which site is performing good and which is performing bad. The more detail, the better.
you can add one code on as many pages as you want. however, people use channels for each site and often use multiple channels for different ad placements to track performance