If I show my national patent application to a company, can they file it as their own in other nations?

If you truly have a national patent (and not a national patent application), then the patent is public knowledge. Anyone in the world can find it, and in most countries (including the US, Europe, and much of Asia) finding it as easy as entering the right query on a web page.

Nationalize PCT Patent Application in Vietnam

If you only have a national patent application, then it may not be public yet. But it will be (in most countries) 18 months after you filed it. So if your outside that window, again, there’s no secrecy to preserve.

Whether or not your patent or pending application is currently public, in most of the world it constitutes “prior art.” (“Most of the world” certainly includes the US, Europe, and most if not all of Asia.) That means it will block any later-filed patent applications that seek to cover the technology disclosed or suggested by your patent application.

To be sure, there might sometimes be good reasons not to show someone your not-yet-published patent application. But if you’re only worried about someone using it as “inspiration” to file their own patent application on the same technology, you need not worry.