You don't need the eReader to gain access to the NES games, at least as far I know. The NES eReader cards are completely independent from the NES games found in Animal Crossing - meaning that the NES cards you see at stores now play on the eCard reader and do not upload to AC. It's possible that Nintendo will eventually release AC eCards that unlock NES games in AC, but that's just speculation.
You answered the second question yourself. Codes are unique to the name and town of the recipient. You could use a code addressed to me - but only if you had the same name and town as I do.
