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Textastic offers syntax highlighting for many languages including C, C++, and Python, but it doesn't include compilers or interpreters due to restrictions of iOS.
You will notice that all apps that support running code - like Kodiak, Codea and Pythonista for example - do not have file download capabilities. So, if I wanted to add the ability to run code in Textastic, I'd have to remove FTP, "Open In", WebDAV, Dropbox and all other means of sharing files with other apps.
These are the relevant points in the App Store review guidelines:
2.7 Apps that download code in any way or form will be rejected
2.8 Apps that install or launch other executable code will be rejected
That's a limitation that is imposed by Apple, sorry.
Yes, running it from within the app on your device won't be possible.
You could try to enhance the file at https://github.com/BlackBulletIV/enhanced-lua.tmbundle/blob/master/Syntaxes/Lua%20(Love).tmLanguage
Unfortunately, this seems to be a limitation of keyboard support in iOS.

Even in Pages, when I press page down on my bluetooth keyboard, it jumps to the end of the file.
I see. I'm using Sublime Text 2, so I guess this is very similar to the View -> Layout menu?

Where exactly do I find this feature in Sublime Text?
For local preview, Textastic doesn't use http but its own preview protocol (urls internally start with "preview://"). So you need to specify the http protocol since it would otherwise try to load the URL using the preview:// protocol which is only for local files.

This is very similar to the "file://" protocol for local files in desktop browsers.