Furd, thanks a lot for your advise. Just in case others encounter a similar situation, here what I found out and did:
Yes, the air filter takes in the air from the back. Here the online manual:
http://www.docs.hvacpartners.com/idc.../31kax-8si.pdf
Yes, the power light only goes on if the air cleaner is operiation, which starts about 5-10 seconds after a heating cycle. So the furnace controls and powers the air filter. I still don't know what the hole on the filter's side would be good for.
I have been running the air cleaner for 2 month now without cleaning, I think I should do that soon. I it's very dirty, I might replace it with the recommended box filter.