Since members can subscribe to individual forums and can be updated via email regarding activity on those forums, do you know if it's possible for us to offer that functionality on our site -- so they can bookmark individual forums and get activity updates on their member homepages?

Eve only supports email for new content notifications. It sounds like you want to display the notification on a web page?

Correct. We want to be able to display the notifications on a web page. Is this possible?

No. At this time, Eve only supports e-mail as the delivery method for notifications.

Is this a feature that we can request be developed for a fee?

Our Enterprise customers can request customizations through their Account Manager.