Where exactly can Snare! affect the Runner from?

1) The Rulebook states specifically that the Runner does NOT reveal cards accessed from R&D

1a)Subquestion: Does this mean that all other accessed cards are revealed to both players?

2) Snare! specifically states in its effect text that it does get revealed from the top of R&D when accessed, supporting the statement in question 1a.  It also specifically states that it's effect does NOT apply while in Archives.

Based on these facts, I assume that should the Runner access Snare! from any central server (with the exception of Archives), or any remote server, that he/she will be affected by Snare! Is this correct?

If a card overrides the rules. The card wins. So under normal circumstances cards from R&D do not get revealed to the corp. Snare is an exception to that. 

As for your question 1a other accessed cards both players would be aware of. The corp knows what is in his HQ and his Archives and his remote servers. R&D is the only server the corp does not necessarily know what is in it unless he has used some sort of a card search ability.