|Generally you want air coming in the front and going out the back. So fans in the back of the case should be blowing air out and any fan in the front should be pulling air in. |
If you can't tell which way a fan is blowing, take a look at the center hub. In all the ones I've comes across there is a sticker over that center hub on the 'air out' side. So if you look through the grill and see a sticker, that fan is blowing out.
Some cases have fans in the side. I'm not sure if there's a set rule for them. I think you'd want to balance the air flow so that if (for example) you had 2 fans in the back, one for the PSU and one for the case, then maybe a side fan would be pulling air in.
If you're unsure about which fan is making the noise just temporarily disconnect it. If the noise stops then that one is the problem. For ones you can't get to, like the PSU fan, stick something like a screwdriver blade in to keep it from spinning. Don't stick it in when the fan is spinning, else you may break the fan blades. Put it in and then turn on the PC. Also don't push it in too far or you may contact the PSU electronics.
Sometimes you can lubricate the center hub of a noisy fan and fix it for awhile. However, I always replace the fan, but then I've got several dozen good fans from old systems I've scrapped that I can use.
Oh, and about your monitoring programs that only shows 2 fans: Only fans powered from the motherboard can be monitored, plus there's usually one or two fan headers on the motherboard that aren't monitored. And often case fans are powered directly from the PSU with one of the extra drive power connectors. Those can't be monitored either.