1. When members(photographers) upload images, I want the theme to reject images with less than 300ppi resolution

2. Also, I want to be able to preview the newly uploaded images before they are published and reject those which do not meet my standards. Therefore, I would like Zenphoto or theme to automatically send an email to the member stating why those images were rejected - I will provide the reasons (which can be slected by radio). When rejecting or accepting the images, I want to be using as simple as check marks.

Sorry, quick answer is that nothing of this is possible out of the box.

1. Besides that ppi do not have any meaning on the web as the actual resolution is actually what counts. There is only a quota manager plugin to set a general memory limit. You would need to create a specific uploader to check this. Perhaps by creating a custom version of one of the two included uploader plugins.

2. You can set the default publish status to unpublished using the publishcontent plugin. However whoever has rights to upload has rights to change that status, too. Additionally functionality like sending a mail on rejection again would have to be coded. T

Here you find info about the plugin systems and available filters:
https://www.zenphoto.org/news/zenphoto-plugin-architecture/

Also reading the theming tutorial might be useful: https://www.zenphoto.org/news/theming-tutorial/

This was good reading on the subject: http://www.rideau-info.com/photos/whatisdpi.html

So, an image needs to be like 3264 x 2448 pixels to have a 300 PPI when printed on 8" x 10" paper. If all you are doing is viewing the images on the computer, the PPI is irrelevant.

If the OP is printing the images, then checking for images of that size would work. I've noticed in Irfanview that some images have a DPI value stored in them but it doesn't always match when compared to the dimensions.