Severance is pretty common, and some companies will just keep you technically employed (and thus paid, and even given health insurance) with no expectation of you doing work or coming into the office. Three months is definitely on the generous side, but not that unusual from what I've seen and heard.
Yep. Severance is pretty common when employees are "laid off" i.e. their employment is terminated not because of employees fault. And generally, you are informed of it, and your credentials and such are revoked almost immediately.
Quite different from when you voluntarily leave, when you give notice and do knowledge transfer and such. I imagine that is because the employee is unlikely to do anything bad, since they likely have a better future.