Error: SyntaxError: Unexpected token

Your error sounds like the Ajax services is returning HTML instead of JSON. Usually this is due to an unrecoverable PHP error. We need to find out what that error says. You can do that either by looking in your error logs, or inspecting the Ajax request in your browser dev tools.

If you can tell me what the error says, I might be able to help.

In answer to your second question – updating the plugin will probably overwrite all existing files including PO and MO files.

If the plugin update adds new translatable strings, those changes should be reflected in the plugin’s own POT file if it has one.

I’d recommend backing up the PO files you’ve modified and putting them back after the update. Then opening each one in the Loco editor, running the “sync” operation and then saving again if all is well.

Nearly there.
If you select that item and hit the Preview tab, you will see the rendered HTML for the error, this will probably contain the words describing the PHP error.

I don’t follow what you mean about not being able to replicate the error.
I can see from your screenshot that the error is there to be viewed. Are you saying it’s no longer happening?

It’s possible the response is cached if it’s not showing up.
Clear your browser cache and try again.

There is nothing to say your problem is the same. This will occur if any Ajax request responds with something other than valid JSON. Please open a new ticket with the output of the offending Ajax request, plus any errors in your log files.