Can options on the Properties tab of a page be restricted to users?

I would recommend using the UI personalization feature for this. Then, when setting this up for give user roles, in the UI elements tree go to: CMS -> ADministration -> Content management -> Pages -> Edit -> Properties -> URLs -> and uncheck the Alias option. Sample screen shot.

Thank you for this, I can now also restrict other problem options in that tab! One thing, the "Page aliases" is the correct option, not sure what "Alias" controls.

It depends whether you mean the "Page alias" field on the Properties -> URLs tab, this stands for the NodeAlias column in the CMS_Tree table and in the UI elements tree is referred as "Alias" or, you mean adding the alternative page aliases - alternative URL paths for pages - this is referred as "Page aliases" in the UI tree. In this sample screen shot, red is the "Alias" and green "Page aliases".

Well, basically I am trying to restrict several of these options (see screenshot) from normal users. I note that the "Page alias" option still shows a [Submit] button when the corresponding Page alieses box is unchecked in the UI personalization settings, although the input boxes & text are hidden so it's fine, but that Submit is probably a bug. Remember that I'm on Kentico 11 so your screenshot is a bit different. https://imgur.com/jqeCRhc

I don't have that Custom Item available as a Property in that screen, see image. screenshot

Also, I'm global admin but all of these things are grayed out for me. How do I get access to edit them?

The "Custom item" was added by me and named in this way to demonstrate where and how to get a custom item into the menu. Also, the custom items are usually done through the CUSTOM module, if you are checking the UI elements tree from a different, non-parent module, they are greyed out. Please, check the project documentation or ask the authors for more details who did what and where.

Not holding my breath but is there an easy way to apply these settings (specifically unchecking two boxes in the screen) to every Role except Global Admin by chance?

I am not sure what two boxes you mean, could you be more specific please?

As discussed earlier in the thread, the "URLs/Page Aliases" and "Security/Permissions" checkboxes in the Roles UI Personalization tree. Somehow I want to make sure those two boxes are unchecked in every Role we have except for Global Admin without having to pull up each of the dozens of Roles we have set up.

For users assigned with global administrator privilege level no permissions, no UI personalization is applied. Global admin always sees and can do everything. For the other roles, the only other way would be creating a code, which will loop through all the roles and update the UI permissions. Please see the API examples.