* is there a way to view sensor data historically and arbitrarily, preferably off device?
* is there a way to use it to control other devices (possibly via a home automation gateway) like my air purifier?
i see that it can be plugged in for power, but also has a battery, which is a nice feature. does that also allow for data transfer?
My experience with the devices that attempt to do the things you want is that they suck.
They do each of those things poorly and their basic detection functionality (most important feature) is also bad. (The reddit thread I linked to has details).
If a device existed that did those things and was actually good I'd recommend it.
As it is, everything in the market is awful.
At least these Temtops have the basic functionality down and do that part really well.
I went with the P10 which does exactly what I want (AQI and PM2.5). It looks nice, it works, and is highly visible from a distance (even has a 6hr battery which makes it easy to move between rooms).
The only other one I'd consider is the one that does CO2.
As a bonus the Temtop sensors are less than half the price of their competitors while being at least twice as good.