The pronounciation is indeed not ideal. You might want to hear «прошлая» at Forvo for comparison: http://ru.forvo.com/word/%D0%BF%D1%80%D0%BE%D1%88%D0%BB%D0%B0%D1%8F/
Translation shows 'past' or 'last', though phrase past night is said to be incorrect.
"past night" doesn't really work in English. You can say "THE past week/month/year" meaning that period backwards from today (logically excluding "the past night"), as opposed to "last week/month/year" which today, Mon May 5 2016, would refer to Mon-Sun/April/2015 respectively.
SO WHAT IS THE DIFFERANCE BETWEEN THIS 2. ПРОШЛЫЙ ВЕЧЕР. ПРОШЛАЯ НОЧЬ. AND HIT ME BACK THAT WAY I'LL KNOW ...
«Ночь» is later than «вечер»:
- «Вечер» is more like ‘evening’, it’s the part of the dark time when people are still active.
- «Ночь» is more like ‘night’, it is the part of the dark time when people are normally asleep.
The borders between «ве́чер» and «ночь» are not clear-cut, just like the borders between English ‘evening’ and ‘night’.
This should be accepted too, since there is no context.
There is a grammatical and a semantic difference between these phrases:
Semantically, «ночь» refers to a later time than «вечер». It's difficult to draw clear borders, and there is a significant overlap, but time like 12 o'clock in the night is probably «ночь» but not «вечер».
Also, «прошлая» can be used as 'the night before' in the actions that happened some time ago (and not neccessarily yesterday), while «вчера» has a meaning of 'yesteday'.
«Про́шлая ночь» is a nominal phrase used as subject (because it's the nominative case), you use, for example, in "Last night was interesting' «Про́шлая ночь была́ интере́сной» (not sure if you need the article in the English phrase). You can make it into an adverbial modifier too, if you want: «прошлой ночью».
«Вчера́ ве́чером» is an adverbial modifier of time. You use it, for example, «Вчера́ ве́чером я ушёл спать ра́но» 'I went to bed earlier yesteday in the evening'. You can make it into a nominal phrase too: «вчера́шний ве́чер».
The only way I could imagine using past that way in English is if you were to write "[the] past few nights".
What would be the difference between? последная ночь and прошлая ночь (I heard последний in последний раз from Vika Daynyeko and this other guy I can't remember the name of)
«Про́шлая ночь» means the night that was before, «после́дняя ночь» the last or latest night of a number of nights.