Not all foreigners need a visum to enter the U.S. You can inform at the foreign affairs department or the U.S. embassy in your home country whether you need a visa or an ESTA application to waive your visa.
Canada has a similar program: ETA
No, for the U.S. (and Canada) no vaccinations are required.
The bike tours are usually offered when the local weather is pleasant. Please note that especially in the interior, the difference between day and night temperatures can be great with some fresh mornings. And ... even in dry southern areas you may be surprised by a rainshower.
To rent a car in the U.S. you must be at least 21 years of age and you must in have a valid driver's license. An international driver's license is not required for most foreigners. At the rental company you must display your passport and credit card. All these documents must be issued on the same name.