We are running an image content system where we allow the option to download the image freely by any user.
Now I want to do the following things for those images:
Are these thing possible by any means?
The way to do everything you asked is if you developed a custom image type and your own image viewer. The viewer is the wrapper for the image that enables the functions you want. You could have end-user versions of the app as well as server versions of the app to be able to show the image online.
This is by no means foolproof, and you would also have to prevent screenscraping so that the image cannot be copied from the screen.
And this suggestion likely does not satisfy all the user experience requirements you likely have but have not disclosed.
DRM is very, very difficult to pull off and even the best in the world cannot do it perfectly. I would suggest that you revisit your need for control over these images and change your business need instead of trying to create a technical control for what cannot be controlled.
No, this is not possible, at least not in the way you imagine it to be.
If your image is sufficiently distinct, then reverse image-search offered by a search engine of your choice may yield results of some usages of your image.
This requires the usage to be public. Usage of your image in private websites, private conversations, etc. is not tracked.
There is no way for you to say "Computer, show me who ever used this image in any way"
This is not possible. If my device is offline, your servers would have no way of contacting my device to ask it if I am using the image. Likewise, just for the sake of argument, your image would have no way of "calling home" to declare it is being used (not that that was technically possible, but even if it were, it would not work offline).
You can't. And even if you could, I could simply make a pixel-by-pixel copy of it, which would then be a plain image file, and there is no way for you to instruct my computer (without the usage of vulnerabilities) to delete an arbitrary file.
TL;DR: "Are these things possible by any means?" "No."
An image is inert data: it is not a software that is executed by a machine. An image cannot "call home" when accessed. Moreover, as MechMK1 detailed in length in their answer, you cannot never prevent someone to take a picture of your image.
The best one can do is prove the ownership of the image when litigation arise. Steganography and watermaking are the two main methods used to embed a proof of ownership inside an image (or video). This is what the main providers of stock images do. This is akin to put your signature in the image, but it can be done in a very subtle manner, almost invisibly. Some of those methods can withstand some basic image manipulation (resizing, cropping, blurring, etc.), but none are foolproof. Like a signature made by a painter on their paintings, it is not magic and will not help the painter to know where their paintings are.
