Is it possible to open an HTML file with a text editor for example so that I can edit it's source?
Sure. First find a text editor that you like, then launch the editor and open the HTML file.
Many editors will also show up as an option in the launch menu for HTML files if you open them from a file browser, so you may be able to just find your HTML file in your file browser and select your text editor when you open it.
Edit: Per your comments, if you're looking for an "Open With" style menu then I can recommend File Expert. You can long press on any file and it will give you an "Open With" option which allows you to choose from the list of your installed applications. There might be other file managers that do this, too, but I'm not sure. Astro has "Open As" which is a bit more limited since it gives you a list of applications based on the file type you choose (text, music, video, image).
Use the touchqode app to see a nice code editor including syntax highlighting, a special keyboard and code recommendation.
Take a look on Android Web Developer. I am developer of this application.
With this app you can see the result in application or in external browser (e.g. Chrome)
Hope it helps.