You can add custom syntax definitions to Textastic by using TextMate bundles. See

http://www.textasticapp.com/v4/manual/lessons/How_can_I_add_my_own_syntax_definitions__themes_and_templates.html

A quick search for "typescript tmbundle" in Google brought up this TextMate bundle which should work:

https://github.com/stoffera/textmate-typescript 

(you need to replace the symbolic link at TypeScript.tmBundle/Syntaxes/typescript.tmLanguage with the actual file though...)

Does it work with another, maybe more simple file?

I just tried it out with local preview of local and iCloud files and it worked for me. You do need an internet connection that can connect to https://getfirebug.com/ for this feature to work.

I did exactly that.

In step 5, if I just tap on the "Done" button to dismiss the preview screen, the next time I still get the file "000.htm".

If instead I tap on the address bar and bring up the keyboard (maybe by accident) and then tap on the Done button (even without pressing any key on the keyboard), the next time it shows the "copyright.htm" file. Maybe that it was happened?

As I explained above, this is a feature, not a bug :) - if you make sure that you don't tap on the address bar, it shouldn't set a new preview file. To revert it, just tap on the address bar, tap on the "X" button on the right side of the address bar and press "Go" on the keyboard.

So, the address bar shows the wrong file? This hasn't occured on my device. Can you send me two example files where this happens?

"y.html" is only used the next time if you manually tapped on the address bar and hit return. Then this is saved as the file to preview instead of the original file. If you just hit "Done" to dismiss the preview screen, Textastic will use "x.html" the next time.

You can restore it to "x.html" by clearing the address bar using the "x" button in the address bar and hitting return on the keyboard.

The reason for this features is this: suppose you have a file called "style.css". If you try to preview the file, you will only see the contents of the CSS file, but you probably want to see how the styles affect a html file. So, you open the preview screen for the file "style.css", tap on the address bar and enter the path of a html file ("example.html") that uses the CSS file. If you hit return on the keyboard, the html file will be opened. The next time you preview the CSS file, the HTML will be opened and you can quickly see how your changes in the CSS file are applied to a HTML file.

I'm not sure how this could work. The browsers can't view files in other apps due to sandboxing. You can upload the file to a HTTP server and then open the url in any of those browsers.

Textastic only supports syntax definitions and symbol list definitions in TextMate bundles. Commands and snippets are not loaded from bundles because many of them would require a shell environment which is not available on iOS. Textastic uses its own code completion file format which could probably be used to write a code completion definition for Node.js: https://github.com/blach/Textastic-Customization