"At the very moment" does not mean the same thing as "right now". You use it to compare when A happens when being compared to when B happens. "At the very moment that the accident happened, Alice was leaving her job." If you wanted to say the same thing as right now, you would say "At this very moment."

Yes, they are similar. "At this very moment" is a lot clearer and has no ambiguity. "right now" is ambiguous