I'd say it depends on the use case. In some instances a comment is submitted to intrigue other readers, while in another scenario the commenter could be asking a question that could warrant a quick reply. I think flexibility is the answer here, let the admin decide how often to be notified. The email to other commenter seems more of a guess to me, but I'd think daily/immediately would be my default method. It's safer to have more timely notifications than letting them get stale. This also helps the admin appear truly engaged with users.
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