Currently, the newsletter is sent free to members and donors. Could the newsletter be offered to the public by allowing them to subscribe to it for $x.xx a year? Are there mailing restrictions in doing that?
You need to download the various publications from the postal service and check the regulations about advertising.
The second question is about unrelated business activity which could apply to both the advertising and the subscription model you are considering. Here is our article about unrelated business income.
I hope this info will at least point you in the right direction. As always, please check with your lawyer and your accountant for definitive advice.