IMHO learning any other technologies will make you better with FM.
In addition to becoming well versed in Relational Database practices and theory I would tackle Java and C/C++ just because they seem to be the most widely in use programming languages right now but no matter what you choose it will be of benefit because you'll be able to think outside the FileMaker paradigm.
If your client says, I need to do this....
- You have options of Custom Functions, Plug-ins, AppleScript/VB script, WebDirect) that can be done IN FileMaker.
- If the integration uses other apps (Custom Web or Web viewer extension, XML &/or JSON, Excel, xDBC/SQL, etc.), then you need to learn (or find a compadre with those skills).
But that's me and what I think will extend FM the most.
Interesting, I'm a programmer from back in the days of chads and punched cards.
I never had a reason to get into XOJO. But it is a possibility for those who read up what it can do and have the need to get into it.
Well, I have a couple of clients who use Xojo and FileMaker. Each tool for the tasks it's better for.
And I make plugins for both. :-)
Along those lines and for the .NET minded folks, SharpDevelop and its successor Xamarin:
Does similar things like Xojo.
When it comes to keep track of technologies and how they are trending I always turn to:
In answer to your first question, I would venture to say that the majority of FileMaker developers I have encountered have little or no background in other programming languages and it is indeed possible to be successful as such. It's helpful to at least know what's out there and have some idea of where it might be useful, especially when you run into a situation where your FileMaker solution is not performing well or you can't find a way to solve a particular problem. You'll have a head start when you start googling, and when you're calling a consultant to help you with the tricky bits.
As to what to learn, I agree with what's been said above.
SQL is immediately useful using FileMaker's ExecuteSQL function.
XML can be handy when communicating with web services. Ditto JSON, but FileMaker has native XML import/export that can do amazing stuff combined with stylesheets (XSLT).
PHP can be used to build websites via FileMaker Server's custom web publishing (CWP).
But... if I was really going to delve into a programming language today, it would probably be: Swift. The iOS market is huge.