The Settlement Discount codes that you use for the BP supplier can be used be used for more than just payment proposal. They can be use for the manual check, wire transfer, etc.

If you are new to Sage X3, have you taken advantage any of the great classes that are offered in Sage University? There are a lot of features you may be missing out on without going through training.  This might be a good one for your AP questions: X3 - Sage X3 - AP Specialist: Setup Options, Business Partners and Suppliers.

There is Sage Knowledgebase article ID 18581 HTG - Setting up Discount Terms which should help you set up the discounts. One thing to note as you set up this discounts is whether you are going to base the term on the invoice date or the due date.

YES you can give discount directly on payment.  I was going through the same question and then I found a link which helped me a lot.

You can can also refer the same to setup discount on payment.

https://www.greytrix.com/blogs/sagex3/2015/10/29/how-to-use-and-setup-the-functionality-of-early-discount-late-charges-in-supplier-invoice/

Please give it a try and let me know if any issue.