Is it possible to apply discount based on specific users or weekday / weekends reservations?

(2) Second, we are wondering if we can set up a system with different payment rates for specific users (i.e. members or donors), as well as different payment rates for weekend and weekday reservations.

I think it is possible to achieve, you can change the rate based on the selection that user makes, you could add the options to the product and then apply the special pricing depending on the selection. 

Here is a guide that will help you to set up special pricing in your form: https://www.jotform.com/help/265-What-is-Special-Pricing 

And you may also provide a coupon code to those special users so they can get a discount when submitting the application form, here is the guide that will help you with that: https://www.jotform.com/help/233-How-To-Add-Coupon-Code-in-the-Payment-Form 

If you have any question, please let us know.