[@robkk Moderator 12 years, 2 months ago]

1) Permit forum users to reply to an email

only plugin i know is https://github.com/rmccue/bbPress-Reply-by-Email

which uses mandrill and postmark for sending emails

2) Send new forum applications (registrations) to the moderator to either approve or disapprove

that plugin user profiles made easy should work on bbpress.

3) Permit forum users to post pictures e.g. .jpgs

you can use the img button in the toolbar which will use a url of a picture then embed the picture in a post.

you can use oembed which is already in wordpress core, where all you have to do is add a link to an image in a post then it will automatically embed. (imgur, flickr, are some examples that can do this.

and yes bbpress attachments plugin