How can I limit the height and width fields of the image field I added to the panel, so that only images of 1000x1000 size can be added, any image added above or below it will not be accepted and will give an error?

I think i need to understand your problem a bit more. Is it when a user uploads a file you wan't to have this validation done or is it somewhere else?

There was (until recently) a package called Image Resizer which I used a few times. A quick look in the marketplace has brought up this package which might be useful:- https://marketplace.umbraco.com/package/badgernet.umbraco.webpicauto

When the user uploads the image and presses the save button

We had the same problem, or not directly the same, but we wanted to create a blurhash value for uploaded images. What we did, was to hook into the MediaSavedNotification and the do the preprocess afterwards. Perhaps you can use one of the Notification streams to do your operation?