Ownership comes first. Ask who owns the code and the design files when the project ends, and make sure you receive the source and the logins to everything. A build you cannot move or edit without the original developer leaves you dependent on them.
Ask how the site will be tested and released. A good team works on a private staging copy, tests on real phones and in several browsers, and releases changes in a controlled way, so a fix never takes your live site down. Ask what happens when something breaks after launch, and who is responsible.
Finally, ask how success will be measured. Page speed, accessibility and search-friendly structure should be checked against real numbers, not described as good. We agree these checks with you up front, and share the results at handover.