Slate is run by one person on one machine. It is free to use and always will be. If it is useful to you and you would like to put something toward the hosting and the time that goes into it, that is genuinely appreciated.
Nothing. There are no paid tiers, no supporter features, no priority support and no queue to skip. Every account gets exactly the same thing whether or not anyone has ever given anything. A donation is a gift, not a purchase, which also means it is not refundable and not tax-deductible.
On Stripe, not here. Slate never sees a card number and stores nothing about the payment - the link below leaves this site entirely. That is deliberate rather than incidental: it is why the Privacy Policy can say this service holds no payment information at all.