So, I'm talking about a image page like this:
https://www.goodfreephotos.com/united-states/north-dakota/fargo/us-department-of-agriculture-research-facility-at-north-dakota-state-university.jpg.php

The image display on that page seems to just a a resized version of the full image when you click on the image to display it full screen. That causes the webpage to be too big and causes long loading times, especially on mobile.

Is there a way on the image page to have the clickable image to a smaller version or a much compressed version of the full image when clicked? I still want the full-screen image when click to actually be the full uncompressed image, just not when its displayed on the webpage.

It's the default in all official themes to use a so called "sized image" and not the full image for the size reason. Take a look at the Zenpage theme's image.php for example.

Thanks, one more thing, does the 1.4.14, work with php 7? I'm going to upgrade from 1.4.11 and want to change from php 5.5 to php 7.

Yes, 1.4.14 works with PHP 7. But before you upgrade a live site server best test locally first especially if you use any older or third party plugins that had no updates.

I'm only using Zenpage plugin, is the "sized image" option in the admin panel?

is the "sized image" option in the admin panel?

It's not an option, it's theming, you have to setup your theme to use it. Again, all official themes don't use the full image on image.php. Please look there or also see the theming tutorial.