The pаз- in разговор and the раз in один раз have different etymologies.
Раз- as a prefix originates from Proto-Slavic *orz-, thought to have originated from a Proto-Indo-European root meaning "part, divide". It's a Church Slavonic borrowing, mostly (but not completely) replacing the native Russian роз-.
Semantically (although not etymologically), this prefix is close to the Latin prefix dis-. One of the meanings of both prefixes is "around, in all directions": рассеять "dissipate", распространить "distribute", разогнать "disperse" etc. Розговорити and розъказати in Old Russian both meant "to make known by telling", literally "to tell around". Later, the two diverged in meaning: разговор and its derivatives came to mean "two-sided communication", while рассказ means "speech, story", i.e. "one-sided communication".
The etymology of the English word "discourse" (whose Latin ancestor literally meant "to run in all directions"), which also means "conversation", is not unlike that of the Russian word.
Pаз in the sense of "occurrence, instance" literally means "a strike, a blow". It's cognate to разить "to strike, to smite" and резать "to cut".
Across the languages of the world, the words for "time, occurrence" are usually not a part of the stable vocabulary. They are frequently formed as metonymies and change quite often, by linguistic standards.
Within the Slavic family, the words for "occurrence" come from roots literally meaning "smite" (Russian, Polish); "cut" (Serbian, Slovene); "way" (Bulgarian, Macedonian).
Germanic: "time" (English); "meal" (German, Dutch); "step" (Danish, Swedish, Norwegian).
Romance: "turn" (Italian), "change" (Spanish, Portuguese, French), "give" (Romanian).
The fact that the current Russian word for "occurrence" comes from a root literally meaning "to smite" and happens to sound like one of the versions of the prefix meaning "apart", is hardly anything more than a coincidence.