"Zeus Pater"
Pater means father. A quick and dirty translation of the phrase would be
father Zeus, and yes, it does appear in ancient Greek sources. eg: "Ὑπερβίῳ δὲ
Ζεὺς πατὴρ ἐπ᾽ ἀσπίδος..." - Aeschylus, Seven Against Thebes, line 512.
Yes, "Father Zeus" or "Zeus Pater" did appear in Greek sources "Ζεὺς πατὴρ".
"Jupiter"
"Sky Father" is a direct translation of the Vedic Dyaus Pita, etymologically
descended from the same Proto-Indo-European deity name as the Greek Zeus
Pater and Roman Jupiter.
This is pulled from a Wikipedia page on "Sky Father." If you translate "Jupiter" to English from Latin, you get "Jupiter," "Jove," or "Sky." However, if you go on Dictionary.com and look at the word origin for "Jupiter," you find that it comes from, "Iuppiter." That word just means "Jupiter," but a Wiktionary is helpful here:
The nominative Iuppiter, for Iūpiter (with shift of the length from vowel to consonant per the "littera" rule), comes from a vocative combined with pater, and essentially meant "father Jove": Proto-Italic *djous patēr, from *djous (“day, sky”) + *patēr (“father”).
So it brings us right back to knowing that "Jupiter" means "Sky Father" and so does "Zeus Pater."
Conclusion:
1:
Yes, as yannis♦ pointed out "Zeus Pater" appears.
2:
Yes, the two terms are related, "Jupiter" comes from "djous patēr," which means "Sky Father," and "Zeus Pater" literally means "Sky Father."