Rather than rendering an avi from premiere, I would make a smaller timeline containing the footage you want to play with and then import this timeline into AE as a new comp. Your fades will be maintained (replaced by opacity keyframes).
Precompose the two layers and then work on them separately. In you main comp, the fade will be as you want it. The 'nets' you talk about are known correctly as masks, so if you want to search for more info on that topic, mask is the word to use. Rotoscoping can be a pain, but here's a
great video tutorial that will help you work faster.
Remember to feather out the mask too (hit M twice with your layer selected).
Simon Bonner
youtube.com/simonsaysFX