Going through one thing at a time. On which hand to use - you can hold the rod with either hand. Your MUST cast off the shoulder where your anchor lies, but you CHOOSE which hand to hold the rod (or upper hand in the case of 2H rod). The pros and cons - for people who can't or otherwise do not desire to switch hands then using the same hand works. For people who can change hands many will choose to cast with the HAND on the same side of their body where the anchor is - in other word NOT to cast cackhanded. While some people can cast cackhanded really well, not doing so will give you a little more room and this will for a lot of people result in more control and more power, but if you learn to do them in most cases it does not matter enough to make a difference. In some cases however, such as trying to cast a single spey with longish line doing so cackhanded may almost be impossible.
The problem with the video is that it is NOT of a snap T, the anchor is downstream not up stream. For whatever the reasons, which we can get into or not, the "reverse snap T" is a fringe cast. I'd like to call it a specialty cast, but I'm not sure is solves any special problem. I have no problems with fringe casts, and am fond of and use several of them myself. The usual cast that would be done with a down stream anchor are, as fishon already mentioned, the double spey and the snake roll. Basically the repositioning move more or less gets the downstream anchor set up the same as a double spey would in same situation.
Probably best to learn the basic casts first, if only to make sense of the terminology. The usulal route nowadays is to learn to do the double spey and snap t from BOTH sides of the river. Then you can fish. Next, in place of, or at the same time you probably should learn to do single speys and snake rolls. These tend to be a bit harder to learn, but are really fun. You should at least know how these 4 cast are done even if you can't execute them all with confidence. That way it is easier to talk about things without confusion.
We could get into the pros an cons of the reverse snap t, but it may be simpler in the context of learning to do then casts you will need to fish to do the conventional snap T. Ultimately of course what ever works for you and what ever you like best is what you can use in the near future. I know a lot of us mix the casts up almost on a cast to cast basis, sometimes just to keep from getting bored. If you want to be able to fish in any kind of wind the you need at a minimum of 4 distinct casts, upmand downstream anchor cast from both side of the river. Hope that help a little.
So the video above is not a snap t, it is a downstream anchor cast, and so should probably compaired and contrasted with the other downstream anchor cast the double spey and snake roll.
Here is a video of a normal snap T by the way....