As it happens the UK's second wave kicked into exponential increase around mid August - the only major public health policy intervention coincident with this was mandatory mask wearing. So yeah.
1 - https://www.gov.uk/guidance/get-a-discount-with-the-eat-out-...
That’s wrong, the opposite is the case. The study controls for this by looking at a synthetic control over the same time period, which consists of other populations without mandatory mask-wearing. It’s an observational study so it can’t control for everything but it does control for seasonality, even if “seasonality” isn’t specifically mentioned in the paper.
Of course this is just my rough calculation (latest population census divided by the number of active cases), and the number is expected to improve somewhat as the amount of population with antibodies increases, but I'm pretty sure masks help.