You can put all the clips in a single sequence, highlight them, and apply warp stabilizer to them all at once. So keep that in mind. There’s no way to batch everything you want to do.
Here’s what I’d do:
Mark all your selects in Prelude and copy them to a new folder. (Or you can just import the originals and mark ins and outs as you please.)
Import the selects into a project.
Highlight all the clips in the project pane, right click, modify and change the frame rate.
Highlight a clip and make a sequence from it.
Create an adjustment layer with all your color correction.
Apply warp stabilizer.
Now make a new sequence with each clip, but at this point you’re just pasting a copy of the adjustment layer and adding the warp stabilizer.
Import the project into Adobe Media Encoder and you’ll be able to select each one of those sequences at once for batch export. The exported clips will carry whatever name, if any, you gave the sequences.