Do iPhone apps use anything other than objective C?

I want to pick up a programming language.
I'm an absolute beginner so I'm wondering if I learn objective C, will I be able to program iPhone or Android apps?
Or are they built with multiple languages?
And something I'm curious about.
When I can professionally develop applications, I had an idea for an app. It's basically google drive. But instead of storing to a server, I want it to be able to access my hard drive directly and then I can open some kind of text file and edit it through my phone. And then when I save it, the changes are saved directly on my pc hard drive.
Would this all be accomplished with objective C? I'm guessing no.

You can use it for both platforms but it is always better for ios.

Objective-C is pretty much only used for iPhone apps. You could technically get it working on Android, but all of the Android APIs are written in C++ and Java so it would be weird to try to use it.

You have a couple different choices if you want to make a cross-platform app. First of all, you could make a web app. You write all your app's code in HTML, CSS, and JavaScript just like a website. Then, you use something like Phonegap to bundle the files together into an app for each platform. Alternatively, you could use something like Mono, which lets you write a C# app that runs on every platform. The disadvantage of Mono is that it still uses the OS's underlying libraries, so you have to write some code differently for iOS and Android. The flip side of that is your app will look like an Android app on Android and an iOS app on iOS, instead of looking like a web page on both of them.

Finally, just a comment on your chosen project: a distributed system like that is very difficult to do. Especially when you're connecting to a device that's behind a router, because it isn't accessible over the Internet without configuring port-forwarding. You also need to make sure your project is secure. Microsoft actually tried something similar to this, called Windows Live Mesh, but they gave up because it was too much effort and not enough people were actually using it. It's a cool project and you'll learn a lot from working on it, but be prepared for some frustration and don't be afraid to ask for help- even the experts find that problem challenging.

I'm sure most of it would be done in objective c, you just need to know how to get it to kind of run the the program putty

Cocoa is written in Objective-C, so there's no getting around making API calls to Cocoa in Obj-C. You can write the app in any language so long as it conforms to the iOS SDK agreement. You're better off writing the application in a C derivative though, even something in Objective-C++ or Ruby.