You can - but unless the site has a clear purpose other than being 'made for adsense', expect to see the cpc they demand be very high. Also - if you are expecting to make money out of using adwords to get people to click on your adsense ads - forget it. the system is deliberately weighted to make sure you lose money.
Yup as Magda says, they will carefully wight the cost to earning ration so we dont all do this and cause google to go bust overnight! Arbitrage does work, you just have to be a little creative with traffic sources and stay away from adwords
Of course you can. Be sure to split test your campaigns and see what gives you the best conversions. Again it all comes down to quality content and also doing careful keyword research to minimize your costs.
Adwords/Adsense is the holy grail lot of people have been searching for, but I guess it will be difficult for someone to have enough intellectual horsepower to out think Google. here is a tip -- there are lotsa different ways of making cool money over the Internet. Try them out!
I believe this type of arbitrage is now against the adsense TOS. As previously mentioned, IF your site has a clear purpose, you might not get banned if you are lucky, but you can expect your CPC and CTR to tank dramatically as the adsense algorithm devalues your clicks and many are determined to be invalid.