The CSS error means your style is using an old style property. You need to update your style for 1.2. That means reverting any outdated templates thereby removing any references to old style properties. Or contact the style author to obtain an updated version of your style.
The missing nav phrases should be fixable by visiting /install and clicking the button to rebuild the master data. If that doesn't work then re-upload the 1.2 files and rebuild the master data again.
Thank you for your kind support @Mike and @Jake Bunce.
I understand that I should take all responsibility for upgrading to Beta version but I can't wait and I really like to experience the new features of XF 1.2.
After two days trying many methods and reading tips and tricks through this forum I have figured out to upgrade to 1.2 beta 1 now:
I deleted all custom styles not only return back to default one but export and delete all others. I also have to delete all other languages. My site use 3 languagues. Finally, disable all addons.
Now I have successfully run 1.2 Beta on my live site and it seem to work fine.