Yes, you can run it on all of your sites as long as they fall under their terms. No gambling sites, no search result pages, etc. Make sure you read their terms very closesly, because they will nick you if you don't.
Yes, different size and color ads can go on each site.
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I use adsense but on one site only. I would recomend that people dont use adsense for sites that sell things cause they could ultimately drive people to your competitors since the ads are content relevant.