It depends what you mean by payroll. Some people expect to just print a paycheck and to take care of the payment processing separately and manually. Others expect to click on one button and that Odoo would automatically connect to your bank to process the payments. The latter is not feasible as of v8.0.
1. There is a payroll module. It is a very low level and generic module. Low level doesn't mean incomplete or bad, it means it is very close to the framework and, hence, very technical. You have to specify absolutely everything in it to make it work. It is so technical that it almost requires to be a developer to configure it (or a very advanced Odoo functional consultant). It is as powerful as it is generic but you will have to know all the rules governing payroll in your country/state/city and input them. For the US, there is no template or pre-configuration module at the time of v8.0. You can find examples of pre-configuration modules with the payroll modules of Belgium, India, or France (eg: l10n_be_hr_payroll and l10n_be_hr_payroll_account).
2. Odoo can calculate it automatically if you input the rules properly
3. Start by installing hr_payroll
4. Not as a certified module at least. On a previous version of Odoo, Novapoint had made a connector to CompuPay: http://prn.to/1Kd1RbU
My general advice is to not use Odoo for payroll purposes at this time unless you are involved in a very large project with a very large customer.
Hi David, did Canada Payroll match with US payroll?
Hi Baiju, It would be similar but the taxes would be different for the US.