Very weird structure, separating 很紧张 without a subject by a comma is just weird.
In English yes, but in Chinese that structure is very common - the subject (我) is obvious.
I believe 明天考试, 我很紧张。should also be accepted. Since 明天有考试 is a very awkward way of expressing this.
Why do you feel it's awkward? It feels like most logical way of saying it to me.
Same here, in fact the opposite is true.