Is it possible to programmatically edit a native Google document, say to make certain words bold or hyperlinks? I know I can export that to some format like DOC or ODT, do the changes and put back. But tried this way manually and saw that I lost the exact look. Could not find any API or object model for native Google docs, although seems there is something for the spreadsheets.
Unfortunately it is not possible to programmatically edit Google Documents (Google's Word Processor document) using a REST API. Only Google Spreadsheet offers such an API at the moment.
You could try Google Apps Script: https://developers.google.com/apps-script/ it is a hosted scripting environment and it offers a Google Documents Service that allows you to edit and manage existing Google Documents.
Lastly you could always upload a document using an open format such as RTF and have it converted to a native Google Documents using the Google Drive API.