"How can I set their KPIs without knowing their roles, gain their respect and lead this new team through a turbulent time in our organization?" - As it stands now, you can't. If you attempt to do so without engaging in your own discovery process (listening and learning) and engaging the team to build mutual understanding re: charter, requisite skills, roles, inter-dependencies, how you can best support their work and establishing group norms (the ways things really get done), it will compromise your credibility as their leader.
Recommend: 1) doing your homework to understand the charter, work and value proposition of this group in context of the business, how they can best be integrated into your group to offer greatest value and get clear re: what expertise you're bringing to the table as a leader (=credibility); 2) talk with all team members to learn about them - professionally and personally - their skills, interests and passions, and their own vision of how this integration can be made optimally successful; and 3) bring the whole group together for a 1/2 day or whole day offsite to develop clarity on charter, value proposition, inter-dependencies, deliverables and KPI's... - as well as the 'soft' side such as collectively desired group norms - and shape agreements re: your expectations as leader, behaviors and values you want to see in the group, and defining how you can best support their efforts. (competent facilitation to help with design/facilitation would likely be helpful, freeing you up to participate most fully in the dialogues). If you demonstrate sincere effort to learning, engaging and leading with integrity and knowledge (and wisdom), the team will see this, appreciate your effort and be willing to follow. (As Warren Bennis said, the one defining quality of a leader is that they have followers). -- Good Luck. Happy to help should you be interested in exploring further.