Unwrapping help in Blender

Hi. Once again I fail to understand why you are trying to unwrap a mesh that is already perfectly unwrapped both in uv_0 and uv_1. I also do not understand if you are talking about uv_0 or uv_1.

1). You must have not selected the vertices properly. Do that with Limit selection to visible turned off or in UV editor;

To avoid moving the vertices along the borders of the uv islands of the connected pieces, either select the uv island in Face mode or disable sync and sticky selection;
3). UV mapping is a process of projecting a 2d texture on the surface of a 3d model. We create a 2d representation of a 3d model and align it with a texture. It can be done is reverse as well, as in, we create uvs first and then create a texture using uvs as a guide. It is not a texture, not a hidden layer, nothing of sorts. It just tells the software how to project a texture on the surface of your model. The uv_0 map projects textures, the uv_1 map dictates how deformation maps will be applied;
4). Not wanting to watch non-sims related tutorials is the biggest and most common mistake creators make. People who make introductory tutorials for Blender or specific topics know what they are doing. They also understand that someone who decided to watch an introductory tutorial most likely knows nothing on the subject. They explain everything there is, not only how to do a specific object. Most TS4 creators watched one tutorial where an author made a specific garment for ts4 with no proper explanation, recreated it and decided they are competent enough to make their own tutorial that is identical to the one they watched. It does not matter whether the person in a video is unwrapping a t-shirt or a tank, all of it is done by the same logic and serves the same purpose. For things that are unique to ts4( like why do we need a uv_1 map), yes, watch s4s tutorials, general concepts ( uv mapping ) - the chances you'll find anything substantial among ts4 tutorials about that are very low.
Watch this video starting from 00:11 to around 10th minute, after he starts repeating the same thing you can stop