You can whatever you want, as long as it's web-based.
Well yes, as it comes from the box. However open your browser and tick "apps that work off-line" and you can find a lot of them. And they do work. Inserting a large-capacity SD card is essential.
I am surprised nobody has mentioned the paucity of USB connectors on Chromebooks, had they done so I would have riposted that connecting a hub solves that problem. Add a mouse, keyboard and big screen and you have something not unsimilar to the large PC that sits on your desk all day and is also connected to the 'net full time.
Google knowing everything about you ? Well, really, I'd never have thought it
Next thing is you'll be saying they sell that data and make money from it.....