The police officer will certainly write down my address, so they will send me some notification, I presume? If i'd pay the fine as soon as I get notified about it, the warrant for my arrest will be dropped, I presume?
Yes – payment of the fine constitutes a “guilty” plea and will close out your case. If you do receive a ticket, it should have payment information on it (a number to call to figure out your fine, payment address and accepted methods, etc). You should be able to arrange for payment before leaving the U.S. – possibly by credit card via internet or phone (not sure if your card will need a U.S. address).
I’m comfortable driving up to 10mph over the speed limit; above that, just make sure that you’re not the fastest or most aggressive car on the road. If you do get pulled over, simply remember to be nice and polite. The policeman will ask for your driver’s license, car registration, and proof of insurance. He will probably take those items back to his car for several minutes while he checks the documents. If the he questions anything, just explain patiently – your demeanor more than anything else will determine the outcome. As an out-of-town guest, there’s a good chance that you’ll receive a written warning instead of an actual ticket unless you get angry or otherwise have a bad attitude.
In the absence of erratic or reckless driving behavior, you have a very slim chance of being pulled over. Enjoy your trip – it should be an incredible experience!