I slightly disagree with other posters. He has booked to stay in your place as a guest. He hasn’t booked a venue for what sounds like a commerical photoshoot.
I presume you have access to the interior of cottage to know he has an assistant (did he book and pay for two?) and equipment. If he hasn’t booked and paid for the assistant you can boot her out on these grounds. Can you clarify how you know he is doing a photo shoot there.
In your shoes, I would speak to him and say he booked as a guest, and you haven’t given him permission to, nor did he ask to carry out a photo shoot on your premises and that you are disappointed and upset that he felt this was an appropriate thing to do.
First I would call AIrbnb explain the situation and ask if it is grounds for cancellation.
It is outrageous of him to do this, but photographers do it because its much cheaper than paying commercial rates to hire a space for a shoot. I would also say that he is not allowed to use photography of the interior or exterior of your premises for commercial purposes. And that he is not allowed to move furniture/accessories in the property without your permission.
If you don’t want to boot him out make him pay for the commercial hire of your place for the shoot in addition to the cottage hire.
Someone on here did this recently. Have a search on the forums to find her post (there are quite a few similar ones too you could have a look at).
I would definitely mention this in your review and give him the thumbs down.
Don’t feel pressured into taking a booking by the way.
In terms of the wifi, this is his problem, he should of read the listing and with this bad weather he may lose his connection altogether (here’s hoping )