There is no special exception which allows you to use a work without permission just because it is being used for a non-profit purpose. You may be able to persuade the copyright owner to give permission for a low fee, or no fee, if the use is non-profit, but you’ll still need to get permission.
If there is doubt as to whether the supplier of the material is the copyright owner (for example, where a cutting from a newspaper is supplied for republication in the newsletter), ask further questions about where the material came from, so you (or the supplier of the material) can get permission if necessary.
You can only grant permission for someone else to use material published in your newsletter if you own copyright in that material or have authority from the copyright owner to grant such permissions. If neither of these is the case, you will generally need to refer people who wish to reuse material to the relevant copyright owner.
It’s unlikely that reproducing an image from, for example, a book, newspaper or the internet merely to illustrate a newsletter would satisfy the fair dealing defence for parody or satire. The defence will only be available if the use of the image is fair and you use it for a parodic or satirical purpose.
The “criticism or review” exception in the Copyright Act is expressed very broadly and, as a result, anyone writing or publishing a review will usually be able to use a scan of the book cover with a book review.
There does, however, need to be a “sufficient acknowledgement of the work”. In this case, the relevant “work” would be the cover art, so make sure that you attribute whoever created the cover art under the picture (you can usually find the relevant designer listed in the information on the book flaps).
The mere fact that a publisher has gone out of business does not mean that anyone else can then publish that book.
In many cases, publishing rights will revert to the relevant authors where a publisher goes into liquidation. In other cases, the rights under the contracts will be part of the assets of the relevant company that the liquidator has to deal with as part of the winding up.