Effective site to transfer / display images with client

The answer might be as simple as flickr or possibly iCloud, but I wanted to put this question out there to see if anyone here has some suggestions.

We work with a client whose weekly ad contains hundreds of product photos. From week to week, they will sometimes reference a photo that was used in the past or will provide us with a new photo to use for a product, requesting we delete the old photo.

The ad is for print, so we do have to touch each image that is provided to us to do color corrections, convert to CMYK, mask the background, etc.

With so many images that come in new and others that get deleted, our client sometimes loses track of what images we actually have on file and will occasionally request we use an image that they had requested we trash several weeks prior. We go through a bit of confusion with them when we have to remind them the image was removed long ago. (And they specifically requested we delete images because in the past, we had a problem of accidentally pulling and using images they no longer wanted us using.) This is also challenging when the designer who usually works on this ad is out and someone is else is having to cover the production of that ad who's not as familiar with all the products coming in and out as the main designer.

I think what we're ultimately looking for is an online solution that we can provide our client so they can reference what images we have on file when they're making their requests. It would be preferable if the images could be kept private (as private as the web allows) so that a google search for a certain product doesn't come up with the photos we're using (and hence, we run the risk of competing businesses possibly finding our client's images and using them for their own ads).

Other wish-list requests for this image/file sharing setup would be:

1. Client can easily see and browse their product images
2. The images can be filed in specific categories
3. Client can use the site as the place where they are providing us with the files (instead of emailing them to us), and, of course, we can download the files.
4. Client can delete files they no longer want us using.
5. When we update the files after preparing them for print, they update to the site. (or we just have to re-upload them)
6. The site would be capable of displaying .psd files or .tiff files (because these images, after we touch them up, have transparent backgrounds)

And what would be extremely magical is if we could link our InDesign document to these files while they're online (hahaha!) Okay, that is probably not possible at all, but maybe it is and I just haven't heard of it.

Please shoot other, more brilliant ideas my way. Smack me upside my head if there's some obvious solution out there. Or tell me "good luck, you're dreaming".

Thank you for your ideas / suggestions!