Luckily, unlike automotive mechanics, a velomobile mechanic needs relatively few specialized tools. For the most part, a set of metric wrenches and a normal bike tool (that you may already have from your "normal" bikes), will be enough to do virtually all of the service you are likely to need to normally do.
Building the FAW+ will require a few extra tools, but again these tools are not so rare that most people don't already own them.
We will list/sell all of the tools that we feel are needed for our velomobiles on this webpage.
For most of the tools needed during construction, look at the Builder's-Manual page for recommendations.
Long hex key. If you ever have the need to remove the steering bar or inner stays entirely from the Quest, a 6mm hex key attached to a 2-foot-long extension would make things much easier. This is not something you are likely to need to do often, so adding a temporary extension to an existing hex key when the need arises may be the best path to take.