FormMail's standard features (such as "conditions") can validate the information being submitted. You might need the Computation Module if the validation is particularly complex and cannot be handled with "conditions".
If the merchant script can be called with a simple URL and GET parameters, then that should be easy too, with the Computation Module. However, if the merchant script needs POST method, then you'll need additional PHP code Hooked into FormMail's processing.
We can provide advice via a support subscription, or we can provide you with a quote to get the whole logic completed for you.
Please feel free to PM or email if you want further information.