In the photo above I can name the first 3 intersection
a) Regular intersection
b) T intersection
c) Skewed intersection
I am having a hard time on identifying the fourth intersection, what do you call that one?
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In UK terminology, your separate turning lane would be called a "filter lane" ( see e.g. Collins dictionary definition). This definition doesn't mean that you can always turn in that lane, it means that this lane is exclusively for turning; traffic in it may or may not have to wait for a green light.
I might therefore be tempted to call it a "crossroads with filter lanes". (I would call your situation a a "crossroads" rather than a "regular intersection". But then I'd also use the word "junction" rather than "intersection"...