Can I update a Revit model using JavaScript or python? How can I view the model on a web browser?
Look into Autodesk Forge. It's a web based technology for converting Revit files to something that can be viewed in the browser.
There are also free and open source libraries that you could try like the one from TT-Core called Spectacles:
http://core.thorntontomasetti.com/apps/Spectacles/#secondPage