Should I export all edited clips before final composition?
Would the second method be faster while working inside premiere? I think so since it is already in 1080p and the software is not rendering a preview of noise reduction + stabilization, etc.


Yes… and no. While the 1080p footage may play better in Premiere, doing the post work on all your rushes will chew up your time trying to correct clips that you may not end up using. If you do the noise reduction in After Effects first you will either have to render the clips, or if you use dynamic linking Premiere will be doing the render on the fly, which definitely will slow it down.

My usual workflow is to do the cut in Premiere. The footage will be ungraded, with no post effects or noise reduction etc.. Once the cut is locked off (ish) then I will select any clips that need post-work in my PP timeline and choose Replace with After Effects Composition. This will create an AE comp with the selected clips already cut to length and in order, ready to be worked on in AE. Once I've done the AE work the comp is already dynamically linked to Premiere, so changes I make in AE show up in the Premiere timeline. 

This means I only have to export the final timeline from Premiere, thus saving an intermediate render. Obviously if there's a heap of After Effects stuff happening on it it will slow down your Premiere previews, that's why you do it after all the editing is done and dusted.