I've lost track of it, but there was a study published about this style of filter around the start of the pandemic that suggested it could be effective at reducing PM2.5 and possibly airborne virii. It's a sound idea conceptually -- continuously filtering and re-filtering room air at a high volume is how industrial clean rooms work, and while this is a far cry from a carefully-engineered system like that (you won't have the hygienic surfaces and laminar flow characteristics, for instance), it at least has more than enough airflow to filter a room effectively.

Effectiveness is pretty much entirely dictated by what filter you choose, assuming you don't mess up building it and leave huge gaps. This guy on youtube made a video showing the effectiveness of different filters: https://www.youtube.com/watch?v=XAJ__E-hIJc

I have one with just some cheapo filters in my workshop. Does a great job of keeping dust out of the air for paint and finish work.

second hand information: my sister is a germ-a-phobe and made these for all the family. I'm assuming she knows what she is talking about.

Depends on the quality of the filters really. Also helps if you put a shroud on the box fan so you don't have backflow around the corners.

https://www.texairfilters.com/how-to-improve-the-efficiency-of-the-box-fan-and-merv-13-filter-air-cleaner/