'Do you agree to participate in rehearsal and research shows and interact with technical equipment'?
I am wondering do I need to use 'interact with' or interacting with' here?
You can use either the Infinitive (interact) here, or the Gerund with the preposition (to interacting).
According to Merriam-Webster's Dictionary https://www.merriam-webster.com/dictionary/agree :
: to consent to as a course of action
// She agreed to sell him the house.
: to accept or concede something (such as the views or wishes of another)
// agree to a plan.