A couple of weeks later, I got a message from Airbnb attempting to get my consent to issue her the full refund "before they start a process". 

However, the lender has the option of calling the note if a transfer takes place without his consent.

I am not a lawyer and thus am not sure if it is illegal to run a background check without your consent. 

You can run a criminal check after, with consent.

Tenant agrees that no painting shall be done on or about the property without the prior written consent of the Landlord."

Does the contract allow the contractor to perform work “outside the scope of the agreement” without your written consent?

She will need consent of her broker to do this, more than likely.

Check into using unanimous consent, where all memebers must agree, but this can effect your tax status regardless of your elections.The Operating Agreement is the heart of the business and you should have a good attorney go over it as there are various ways to mess up your tax status with contradictions in the OA or have security issues with more than three members.

We discovered multi people adults and children have moved in without consent/ notice/ in violation of tenants section 8 agreement.

Be sure you pursue this with the landlord's consent!