I think the problems you are describing are newbie errors, and can easily be overcome.
The first time you use a mat, it will be overly sticky, so little pieces will be hard to take off. They sell a spatula to help remove pieces from the mats, and it is very handy. I think
Walmart has them for ~$8. After the first couple of uses, it will become much easier to remove stuff. Then you might have to worry about it not being sticky enough. To delay that, I will wipe off the maps with baby wipes, when I amd done for the day.
Adhesive, for the paper piecings/letters I use either a Zig (this is the brand) Pen, with a chisel tip. Walmart sells these for ~$2.50. Or I also use the Xyron tape that fits the 250 model. You can buy the refill for about ~$5, and not even get the machine for it.
Also, you will have to play around with blade, speed, pressure settings to get it to cut the different types of paper without tearing, and cutting all the way through. Use your scraps to play around with it, to get a feel before you start working on major projects for the page. I think we all wasted a lot of paper in the beginning.