You can access dropbox via their web interface. I don't use one cloud, but imagine it's the same way. By far google drive is the easiest to use from a chromebook.
Yes chromebooks can be rooted... sorta. In chrome OS it's called "developer mode". And you can do all kinds of wonderful and dangerous things therein. The one that I've used is installing a distribution of linux called
crouton which can run simultaneous with chrome os. There's a lot of fun stuff you can do with crouton. Like run a native skype application or run
wine and then run a few windows applications that wine supports.
I do not think that chromeos feels like android. What it feels like is google chrome browser. Imagine starting up your windows laptop and booting into the google chrome browser. Anything you can do on there is what you can do on chromeos. There are a few additional things that you can do, like taking screenshots and managing files and storage. But for the most part it's just like logging into a device that runs google chrome web browser.