I am responding to your questions in the same order as you posted them:
1) For NSF STTR, the submitting organization has to have a PI from the small business, but the subaward must have a co-PI from the partnering institution listed on the cover page and on the subaward budget. (see question #35 here)
2) Yes, NSF definitely allows for teams, and the team strengths are one of the scoring factors in the proposal review process. Just as NIH, NSF allows for Key or Senior Personnel members, all of which require a biosketch to be submitted with the proposal, as well as having a section within the proposal where you highlight the team’s strengths. For minor tasks, you can also use “other personnel” and have them included on the budget.
3) NSF STTR requires a minimum of 40% of the budget to be for the small business, at least 30% of the budget for the partner research institution, and the remaining 30% can be used toward each of these, or any other consultants or fee-for-service providers you require. So NSF STTR also allows up to 60% for the partnering institute.
Let us know if you have any other questions!