There is an adhesive backing on your homemade sticker, but it won't cut around the image as a regular sticker is punched out. So you'll have extra adhesive on a square paper around the image. Once you peel off the backing that all will come off with it, and you are left with the sticky image. I hope this helps.
I haven't encountered that problem but it could be that the roll that you put in the machine that sticks to the paper is old or gotten too hot and made the paper stick to it. If you try a new fresh replacement roll and it sticks too then I would contact the store where you purchased it and complain.
Make sure you have it loaded correctly. Sometimes the top part of the laminate isn't threaded correctly. Take it out completely, see that the machines parts are in place as sometimes the latch thingy(I am not technical lol) isn't pushed in firmly. Be careful not to break it. It must be aligned correctly to work.
The permanent adhesive came with mine. I've created signs by cutting out letters with my Cricut, then putting them through the Xyron to make them stick to the poster board. I've also used them for other Cricut cuts that were hard to add glue from a glue pen. This was a much faster alternative. I have the little X shaped one as well. I make cards more than anything else for the 5" width has worked well for me.