Hello Veehunnoall80
Yes, now the question has been asked a hundred and one times 🙂
1) Correct
2) Correct
3) Yes. But most places are not at the mountain top, thus you need to pay for a ticket to reach the summit.
The only mountains where the SDP is fully valid are: Mt. Rigi, Mt. Stanserhorn, Klewenalp, Stoos, and Rochers-de-Naye.
When using e-tickets, you have to carry your physical passport or official identity card; photos of it are not accepted for ticket checks.
Kind regards,
Roland