Not an expert but I have studied Soviet history and come from a family from the former Soviet Union. So first of all the word товарищ does translate to "comrade" but it has a different connotation in Russian. Whereas in English "comrade" sounds somewhat militaristic and is almost unilaterally associated with the left, in Russian the word товарищ has connotations that make it closer to the English word "companion" or, at a stretch, even "friend". As a child, it was normal for my grandfather to ask me if I was going to hang out with my "comrades" in Russian, and it was meant in the context of friends (this was in the US, mind you). So the word itself sounds a little less overtly political in Russian.

As to how common it was to greet your neighbors and so on, the answer is very common. It was used to refer to strangers if you were trying to get their attention for example, along with other words like гражданин ("citizen"). It was used in place of the English Mr./Mrs./Ms. so where in English you would say Mr. Jones or Mrs. Smith, in the USSR you would say Comrade Jones and Comrade Smith (although in formal contexts, the correct way to refer to someone would be with their Name and Patronym). Likewise, in Russian when referring to officials its common to put a courtesy title in front of their actual title. Nowadays, and before the USSR this was usually the word господин ("lord" or "sire" literally, but closer to "mister" in connotation) so you would refer to a General as "Lord General" or a Professor as "Lord Professor" (this is literally, but a better translation would be Mister General or Mister Professor, like how in the US we say Mister President). In the USSR, "comrade" took the place of those courtesy titles so the normal way to refer to people was "Comrade General" and "Comrade Professor".

So in short, the phrase was very common and used in a wide variety of contexts.