I. "forth, publicly"
II. It always meant "prolong, extend; delay" It just gets used often to say the same thing, in this case "ask publicly [for more time]"
Some things to clarify before I address the questions:
- In Latin, pro does not really mean 8 separate things. It's one or two basic ideas that we can translate 8+ ways.
- You've looked up pro the preposition, rather than pro the prefix.
- pro the prefix, according to Keller & Russell (Learn to Read Latin) has these common translations: "forward, forth; in front of"
And now for each question:
Let's use that first translation of Keller and Russell, "forward, forth." In prorogare we are literally saying "ask forth." A more fun word, promulgare, literally translates "milk forth." But we know it really means to promulgate, report publicly, or expose publicly.
As we can see, pro in both verbs means "forth" in the sense of "publicly."
II. It's not that pro "combines" with rogo differently from the "literal" pro+rogo. Instead, the word prorogo is used more in certain contexts. But what contexts? Let's look at its common direct objects. Cicero and Livy used prorogo to ask for more imperium (the privilege of commanding an army, which has a time limit).
From the Lewis & Short (via Perseus' Latin Word Study Tool):
ne quinquennii imperium Caesari prorogaretur, - lest for 5
years the imperium of Caesar be prolonged, Cic. Phil. 2, 10, 24.
Link to the full lexicon entry. Click on "Lewis & Short" or "Elem Lewis" for the info
I think this example shows how "ask publicly for more imperium" clearly means "[ask to] prolong imperium."
If this hasn't yet convinced you, some other nouns used with prorogo include spatium, or "span/extent (of time)" and mora, delay. Or to use the sense of "defer": dies ad solvendum, day of being freed, and my personal favorite, diem mortis, day of death. And there we have that legal meaning, "discontinue temporarily" from the sense of "delay."
III. Legislative meaning means it's found in legal documents. Probably, it was a common courtroom/legal phrase, like pro bono. There is no reason for courts to change its meaning.