This DIY air purifier could improve your home’s air quality and protect you from wildfire smoke. Here’s how to make it

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.

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.

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/

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.