Things to ask:
Overall briefing on how it works.
Description of infrastucture it runs on.
Anti-spamming techniques that they use, and how they maintain it.
How message sending works - what fax queueing mechanism, what MTA for email? (Big queue in the filesystem, it seems.)
Handling of delivery errors; distinguishing fatal from non-fatal bounces.
Why is the confirmation mail sent as text/plain + text/html? (There's a comment in the source code saying, "and the HTML body for AOL users" -- are there AOL users who can receive text/html, but cannot receive text/plain?)
How much use of FaxYourMP is for follow-up mail? (E.g. my MP sends me a letter and I want to reply to that.)
Notes on using their service:
Ideally, we should grab it as is and immediately use the existing service. Then gut bits of it out and improve them (starting with database of representatives, then other things that need improving). Always better to start with something that 1) works and 2) has years of detailed practical knowledge embedded in it