That's the one I have. However, if you intend to get into the plants as well as the fish, then I would suggest you avoid it. It's good for an unplanted or low planted tank, but for a heavily planted tank the flow is just completely insufficient (hence why I'm swapping it for the EX1200 I have which has much better flow).
If the PF3 says it's 800l/h you should approximately halve that for the actual output. So it will likely be more in the region of 400l/h. Even then that's not bad, but how much water it shifts is not the only thing to assess a filter on. The media capacity is important too, and that's one reason why I like the APS ones - you really can fit a whoooolle lot of media in there!
As for airation, the only thing needed for gas exchange (ie, carbon dioxide out of the water and oxygen into the water) is a good ripple on the surface. The bubbles do very little, except possibly increase the surface area a bit when they burst at the water's surface. Air stones are very pretty, but in a cycled tank with a working filter are only asthetic. If you were to have a filter failure, then they would prove useful as they increase circulation, and if your stuck on a Saturday with no filter until Monday when shops open then you can suspend the media in the tank with the air stone underneath it and it moves the water past the media. Basically, they can be useful... but for specific purposes. If you aim your filter outlet so that it ripples the surface then gas exchange will be sufficient. don't let that put you off getting one if you think they look nice though
Finally, if you purchase a new filter then yes, as you said, you put the media from your PF3 into the new filter and you're good to go. Reduce feeding for a couple of weeks but otherwise everything should be ok. The bacteria is in the media, so you're just giving the bacteria a new house to live in.
Moving away from plecs is fine