Do I trust the FO? I don't think that's the right question. To me, it's how well have Falvey and Levine done their jobs? Evaluating that would require a wide-ranging detailed analysis. While looking at trades and draft choices is certainly part of the matter, this goes far further than that. Who has been hired and how have they performed? This applies to everyone in baseball operations, from the manager and coaches to scouts to player development to clubhouse attendants. Beyond that, for lack of a better way to say it, what is the corporate culture like? Are employees treated fairly and respectfully? Does the FO create an environment in which employees want to do all they can for the betterment of the organization? How well is the organization positioned for long-term success, both on the field and as a business? I'm sure there's much more that someone who understands how large organizations function would look at.
Do the same thing for every other MLB franchise. Then look at how the Twins' front office compares with the other 29 teams.