What questions should I be asking this company in an interview next week?

Just a few to get started, in no particular order of importance (just alphabetical):

• clients: how do they get their clients? How many are repeat clients? How do they build relationships, and demonstrate their expertise? Where does UX fit into their corporate strategy, both for their clients and for the company?
• innovation: how open is the firm to innovation, and how do they demonstrate that innovation? What is communication like? How many tools (systems, apps etc.) are developed by staff, and how open are the management to changes in their tools to improve them?
• selling UX: are designers going to just work on the designs, or are they expected to actively sell UX work, and if so, how?  Are staff encouraged to contribute to the larger design community at large (i.e. associations, etc.) and if so, what support are they given?
• training: what kind of training do people get - i.e. are client services well versed in UX? What kind of continuing education/training do the UXers get? If they plan to expand to more than one UXer, what would need to happen to make that a reality - is it staff, the demand/client projects, etc.
• tools and methodologies: the usual around what software, and why, and how willing the company is to invest in the appropriate tools (i.e. collaborative technologies, etc.). 

Not sure if this helps you, but its a start, hopefully.