Vertex group (colors) doesnt show on Mesh

Hi. The author of the tutorial is using an older version of blender because she does not know how to set up Transfer weights in newer versions and that is a sign of her being a beginner. It is best to avoid tutorials like this because they are similar in their mistakes/misinformation.
- make sure the reference is visible and selectable. in the screenshot it is hidden and that is the most likely cause of the problem;
- select the reference, shift-select your garment, in Weight paint choose Transfer weights, make sure to choose By name (this is another reason the weights could have not transferred, in 2.7 the default choice is different) and Nearest face interpolated (will give you better results if the garment has denser topology that the reference);
- use Clean with All groups ( I’m not going to go into details, but in 2.74-2.79 weights transfer in a way where checking each of them as the author tells you to do is useless. Going through them all is useless in any version, really);
- use Limit total with 4


As for uv_1, you just closed the window with it. Just click and drag in the corner to open a new one and then switch the type to UV editor.

as for the garment not following the rig in blender, it should be chosen in the Armature modifier 

If the author told you to merge the garment with the body, then started transferring data, do not do it this way, this messes up the already perfect data of the body