kinda... you can always use office.com which is Microsofts online version of Office, although this won't work if your offline. Alternately, you can use Google Docs which does have offline support, and it works seamlessly, if you don't like Google, check out the Chrome Web Store for other Apps. For Calendar, you can use Google Calendar, but if you don't like Google you can use Sunrise. Lastly, for offline Mail, both gmail and Outlook Webapp both have offline support.
You can work on certain types of files offline, and you can specify which files or folders to keep offline, but you can keep only up to 5G or 4000 files offline. As of July, 2014, "if you're using the new Google Drive, offline access is already set up. To turn on offline access using the new Google Drive, click the Settings menu in the upper right > Settings > Offline > check the box next to Sync your work to this computer so that you can edit offline." Chrome books will have the "new Google drive", not the so-called Classic Drive (which has different offline setup instructions). For more information, go to google.com/drive, click the Settings gear icon, choose help, and type "offline".
That is a great question that I'm not sure that I can answer. What I do know is this: depending on the wifi adapter the ChromeBook uses, it may be compatible with the internet in China. The operating system may not be compatible with some Chinese applications, that is something you may have to talk to Google about. I would do research on the Wifi adapter the ChromeBook used just to make sure it's compatible, otherwise I don't see how there would be an issue.
I actually did research on that myself I.too have an hp printer it seems the only way to.print is.to setup the google cloud print service which was confusing at first so what I did I watched a tutorial on YouTube and got it done doesnt matter what brand of printer you use as long as you set up the cloud printer service , hope that helps