I'm not 100% on this but I think I have a pretty good idea on how to determine the winding configuration/vector group. Here is one I found on the NETA 3 practice test.

So first you determine which winding is the high side and which winding is the low side because these configurations always have the high side written first even if it's a step up transformer. This is pretty easy since the letters H and X tell you. So the one on the left is the high side and the one on the right is the low side.

Second, We determine how the windings are connected to each other in the high and low side. (Wye, delta, zig-zag, etc.) Again this is pretty easy. The one on the left is a wye since each winding connects at 1 point. The one on the right is a zig-zag since each leg has a 120 degree bend.

Third, we determine if a neutral is present on the high and/or low side. I believe these type of diagrams have the convention of showing an H0 or x0 if there is a neutral. The zig-zag side has x0. So already we know the answer is going to look like 'Yzn#'. We just have to find that number.

I believe vector group numbers are based on the face of an analog clock. An analog clock face is a circle divided by 12 hours. Each hour is equally distant from each other so, 360/12 = 30 degrees. If we imagine that the H2 leg of the high side is pointing to 12 on a clock, where is the x2 pointing to on a clock?

This is a little tricky on a zig-zag, but it's pretty easy to see that x2 is pointing to 11 on a clock. You can use vector math to confirm that x2 is 30 degrees away from H2 but eyeballing it works just fine. Since x2 lies at where 11 would be on a clock in reference to where H2 is, the configuration is determined to be Yzn11.

You don't always use H2 and X2. You just always use the one that's 'pointing' to 12 as your reference. If you were to rotate both windings 120 degrees, you'd get the same answer using H1 and x1.

This is a Dd6 because they're both delta, contain no neutrals, and x2 is pointing to 6 while H2 is pointing to 12.

This is a ZNy11 because it's Zig-zag to wye, the zig-zag has a neutral, and x2 is pointing to 11 while H2 is pointing to 12.

I'm not sure how to answer the T-T transformer questions. I'll have to do some digging for that.

This is the reference I used

https://law.resource.org/pub/in/bis/...026.1.2011.pdf