There is a great deal of debate as to the pronunciation of classical Greek (and what I said earlier I meant to apply only to general American pronunciation). I'd heard that alpha had two distinct sounds, but other theories do exist. It's probably just my archaicism coming across, but I'd rather not pronounce according to the way the Vowel Shift has gone when there's a perfectly good Greek cognate to base my pedantry off of. And I may be wrong about the accent of ouranos, I don't have any of my references with me, but I thought I remembered the accent being nearer the front. If I remember my rules correctly, it's unusual to have an accent on the ultimate in a three-syllable word; I guess because the penult and ultimate are both short it might be on the penult, but I really would have thought it was on the antepenult.
(1) I'm not aware of any evidence that Greek /a/ and /aː/ differed in anything but quality—they were more like the vowels of 'cut' and 'cart' (in my accent).
(2) The use of the vowel /eɪ/ (the FACE vowel) in Modern English is irrelevant: this comes from the Great Vowel Shift of about the 1400s, when long /aː/ changed to long /eː/ (and subsequently diphthongized).
(3) Classical Greek had a pitch accent, and our�?nós had a high tone on the final syllable. In Modern Greek (which is irrelevant to English) this has become a stress accent, but generally on the same syllable.
Remember, however, that long a in Greek is the difference between 'father' and 'cat'. If it were truly what we consider as long a, it would be transcribed ē (and often those are mispronounced as an English long e!) Based on the pronunciation of the Greek, I would recommend 'oo-rahn-us' with stress on either first or second syllable (the Greek would actually take the first, or sometimes third depending on declension, but the second sounds better imo...)
The Greek for "sky, heaven" was our�?nós with a long /aː/. This would give Latin Ūr�?nus with stress on the -r�?-, and thus the usual English pronunciation /jʊˈreɪnəs/ or /jəˈreɪnəs/. However, Latin actually used a short /a/, for reasons I can't venture at, so the Latin Ūrănus with initial stress is the origin of the alternative English pronunciation /ˈjʊərənəs/.