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
I would like to follow up with number two on this list.
It took a whole matter of an hour after I installed my bbpress for a spammer to register. I deleted them immediately, but if I wasn’t at the laptop he could have immediately made a mess of the new forum.
I would like the ability for new registered users to be in a specific moderated role where all posts they make are held in as moderated (private) until approved. And then, when it appears they are legit and not spammers, I can move them to the standard user role. Is there a way or a plug-in to do this? Thank you.
I use the plugin Confirm User Registration which does exactly what you originally asked for.
You do need a small mod to get the participant part to work, but if you want to approve all users before they go live, then try this and if it’s what you want come back and I’ll give you the mod that makes the bbpress participant role work.
I also use SB Welcome Email Editor to make the wohle thing make sense to the user
I have added the “Confirm User Registration” deal for my website. I will see if that helps, and if I want more functionality with this I will come back in here.