I think, and this is not a sure thing, but, I have done FP through the copier, but only with fabric attached. I think the plastic would melt off the FP if done alone due to the high temperature in the copier, just a thought. The fbric creates a barrier for the plastic side of the paper. You have to be sure the freezer paper goes in with the paper side in the proper side up or down depending on the copier.
You could press a cloth to the paper and run it through the copier to print your pattern and then peel the fabric off and reuse it over and over. This is just a suggestion to try. I would hate to see you ruin the copier.
As far as cutting the paper to size, it should work as long as it is not to bib. A smidge to small should feed okay. I cut newsprint all the time to go through the copier and it is never perfect but works.
Another ? I would have is why not just use the newspaper to print your pattern and do the fold and sew process. I do it that way.
peace