Is should've ever correct as a contraction in proper English usage?
English language contractions are generally regarded as informal. In formal English, such as in a business letter, they are not used. In everyday English "should've" is no less valid than any other contraction.
Depends: some interpretations of "proper english" don't allow for contractions. As far as contractions go, however, "should've" is acceptable.
Yes, it is, but not as frequently used as simpler contractions like it's, can't, don't, etc.
In spoken English or in writing answers on YA.
Yes, it is. It is correct wherever the phrase "should have" would be correct.