Would it be wise to run a fanless PSU in one of these cases? I read that fanless PSU's require some moving air. Due to the 3 chamber design, the PSU will be left by itself. Would it be OK, or would it cook?

If it is an old (+5 yrs) passive PSU then you might expect it to require additional airflow. Modern passive PSUs produce so little heat that they do not need additional airflow and in addition it is not a good idea to blow a load of hot air into them.

The NSK2480 does not have the best level of venting around the PSU but this should be fine if you are only running a media PC with a relatively low powered set of components. Ask it to supply 400W and you might have a lot of heat building up but naturally at 100W there is less heat fighting inside the PSU and a little heat from a hard disk to the front of the PSU.

I was looking at getting the Seasonic Platinum Fanless 520W. Would it be ok powering an i3 3220, a 6870, and some hard drives?

The 520 is a bit over the top for that. Your total power draw will be less than 250W. The Radeon 6870 does have 2x6-pin power connectors which does rule out using some PSUs without an adaptor but you should at least drop to the Seasonic Platinum 460 fanless. It'll save you some money and be more efficient in this power bracket.

Thank you, A Seasonic 460 it is. I was originaly planning on a 400, but I realized it didn't have the 2 6 pin PCIe connectors, so I moved up to the 520.

what does a regular PSU do that a passive PSU Cannot do?

Blow.

Or suck. Depends on your perspective.

according to silent pc review, there is no good silent PSU, they all sucks

No, modern PSUs with fans all work by positive pressure cooling so they blow, not suck. I still have a very early 250W ATX PSU where a 92mm fan was mounted onto the underside of the PSU and it worked by negative pressure, exhausting air onto the CPU to increase cooling. Most early ATX PSUs worked this way and hence sucked (negative pressure). I have since modified this PSU with a 120mm fan mounted internally, thus cooling by positive pressure. Therefore it no longer sucks but instead blows (postive pressure).