Is an employer allowed to terminate an employee's online access to payroll information, if the employee has already been terminated?

There is no "right" to online information. It may be a company policy to allow access. The company can decide by policy who can see, and when it can be seen.

Yes, normally a terminated worker loses access.

A terminated employee has only one right: to get a W2 by 1/31 of the following year. Make sure to send them your address if you move.