Payment, how much money should I ask for longer drop-in shifts?

There is never a set rate for extended visits, 4x14 is probably too high, many sitters charge the boarding or day care rate but since you don't offer those services I may suggest 35 for the visit.

You might want to check to see what other charge for daycare and then use somewhere around that amount to establish your rate for this client. Since you would not be able to service other clients, you should also take this into account.