The app / website would be able to match like minded people with extra tix or needing extra tix to exchange those tickets at face value... Other aspects to this of course but not much room to offer details.
You would have to apply for non profit status, which means you would have to incorporate as one of the 29 different 501c classifications. Since I don't know of the details of your business model I would not be able to say for certain, but it is contingent on your company fitting the description of one of those 29 classifications.
I imagine it would be rather hard to get traction with this.
Yes, this can be structured as a Non-profit for promoting the arts. You will need to build this carefully and be true to the meaning of being a "non profit". No scalping of tickets etc.
I have a Masters in Non Profit Management and have created and run numerous non-profits.
I'd be happy to walk you through the process of setting it up and watching out for pitfalls. Including filling the necessary paperwork, raising money and creating a board of directors.