Can we push Payment forms and Merchant Facilities created in Sandbox to Production?
It is not possible to push to production. The safest way is to recreate the forms in Production.
You could potentially use data loader to migration Merchant Facility, payment form, payment options, letter objects and re-link.
Note, on the Merchant Facility, there is the Organization Id field. You'd need to update that too.
If you've done a number of changes using the Payment Form builder, you could add the Payment Form JSON to the page layout and then copy/paste that to the production version.