grammar - Simple explanation of the many functional uses of 'should'?

[User John Lawler]: So how many named special cases of each modal verb are there, in toto? There's
1. subjunctive should, and
2. mandative should, and
3. putative should, at least;
and I s[up]pose 4. Should we? is suggestive should, and
5. Shouldn't we? is tag **should**, and I can think of a lot more.

I ask about only operative uses of this modal verb including literary and formal usage, but please omit anything obsolete. I'm trying to classify them and learn the formal terms describing each.
Are there any apt others in addition to the ones above? (I added the enumeration below)

1. What's 'subjunctive should'? Whenever should is conjugated in the subjunctive mood?
5. What's a tag **should** ?
6. Where does should/would feature? What's it called? This should is detailed in point 3 under 'Usage Notes' on page 1 of 2 or the last para herein or "should like to" vs. "would like to".