The first sentence is an example of negative inversion: after a negating, adverbial word or phrase, the subject and auxiliary (here the verb "to be") are often reversed in order:
There are no rules in any state
In no state (negation) are there any rules
In no way am I going to eat my peas!
Never has he travelled by bus.
Not until she went to France did she realise how much she loved baguettes.
The main reason to use this inversion is for formality; rarely is it used in everyday speech.
There are exceptions to this rule and times when it is optional. See Negative inversion for a good overview.
In your second sentence, "there", which would act as a subject, is simply omitted:
Between these two extremes (there) is a compromise view.
"There" in this case is the existential there - it is not an actual subject, though it can stand in for one. In your example sentence, it is simply not necessary.
In the garden (there) was a dog.
On the wall (there) was a giant spider.
Again, this is not common in everyday speech, and is usually used in formal circumstances or storytelling.