The search function does work, but you have to be more specific - there are probably tens of thousands of posts that have the word "vinyl" in it. I don't know if you are cutting vinyl off sheets or a roll. You do not have to use a mat if they are 12x12 squares for instance, but you might want to. I do not cut vinyl off the rolls for instance as I just use it for little things - to enhance cards or words here and there etc.
Under the FAQ section in the learning center you will find suggested settings for different media that you can download, but remember they are just SUGGESTED settings. Some cut vinyl at 4 and others at 20. A lot depends on the placement of the blade in the blade holder (the height of the blade) etc. Use your test button to cut rectangles to get the best setting for your machine. Go through the learning center thoroughly so you understand how to determine how best to cut things.
You should find many of those helpful.
Also, there are a wide variety of videos under "Broadcast" on the forum and they are also on YouTube.
The transfer paper is for removing the vinyl from its backing and placing it on the surface you want so it will remain intact and not stick to itself. No you don't cut that on the machine.
There are examples of cutting vinyl on
www.silverbulletcutters.com as well.
The best teacher is truly trial and error but this will get you started in the right direction. And be sure to use your setting tool.