This is very cool technology. Think of the possibilities: access to a blockchain ecosystem just by pointing a browser to a website. This is something your mom could do.
Definitely try the beta net.
In respect of wallets, I was able to find the following info:
"Your Keys are stored in your browsers offline data. If you close your browser or clear your browser history your Keys will remain stored and your account accessible. You can use your Keys to start mining in any browser or device, however there is no UI and logic for that yet but we are working on it."
How to get your private key:
"Currently, just type Nimiq.get().wallet.keyPair.toBase64(); (cf. our API doc) in your Javascript console that you can open with F12."
Disclaimer: I am just a bot trying to be helpful.