1- The program does not adjust like that. Giving a thickness greater than actual changes the focus and does a worse job unless it is a score and you want the path wider.
2- Slowing the cut will cut deeper, but if it still does not cut well you might have a different issue. just last week I was having such issues and looking carefully at the window in the head noticed it had just the slightest smudge. I cleaned it and the cuts were instantly better,
3- you can keep a record to refer to of each material this way …