Do damaged level 2 or higher barracks use food?

Yes they use food, quite a bit of it actually.

You can disable them from the province list without repairing them.

Yeah, since the update from May 23, damaged buildings can alike as undamaged ones also be activated / deactivated directly in the province.

I’m on the mobile app. I don’t see the deactivate button for barracks that need repair. All others have been deactivated.

You can only do it from the second tab of the production menu not the first tab for the mobile app. Sorry I am not currently in a match so I cant share a screenshot

I don't think there is a way to do it on the mobile client. I have had to switch to desktop client to disable a damaged (>lvl1) barracks. I assume naval base and reactor would be the same.

If that is the case you can switch your mobile browser to desktop mode to do certain things. I have instructions for that in a lot of posts.

Not all features are implemented yet on mobile.

You can do it on mobile I have turned off bareacks from mobile many times. When you go to the production menu and you get the list of all your cities there is a second tab in the top of that screen when you select it you can disable buildings from there be it ports, barracks, etc

If there is a way to disable a damaged building on the mobile client (not the app) I'd surely appreciate learning it. Sure, it can be done by switching to desktop mode but that can be a chore on a smartphone.

Here's a province list on mobile client - Vilnius has a damaged lvl 2 barracks. You can enable/disable from this screen on the desktop client by clicking on the building, but not on the mobile client.

Here is the Vilnius construction screen. No ablility to disable barracks.

This is the construction screen from a province with an undamaged barracks - with the enable/disable button.

Where is it that a damaged building can be enabled/disabled on mobile?

Perfect you found the correct tab. So from the list of buildings you can press on the barracks and you should see appear a red bar over the image of said building

I can't make it happen. Tapping on the vilnius barracks on the province list screen only selects the province. Press and hold on the barracks does nothing.

Crap you are right just tried it myself it no longer works from province menu, now you have to manually select the province from the map and select the barracks and then deactivate them from the building menu.

When you go to the map and select the province and go to the building on the constuction screen for a greater than level 1 barracks that is damaged (or naval base and reactor) on the mobile client, you'll see a screen like screenshot number 2 in my post above. There is no enable/disable button.

So, as far as an answer for the OP - currently there does not appear to be a way to disable a damaged greater than level 1 barracks on the mobile client. This can be done by switching to the desktop client on the settings menu and disabling the building, damaged or undamaged, in the usual ways.