What does "enable DOM storage API" mean?
I believe this functionality is irrelevant for websites that do not use the HTML 5 specifications, since it is part of that spec. I would imagine the main thing to look out for when enabling this API is that it would then allow ANY website that takes advantage of DOM storage to use said storage options on the device. I would imagine it is disabled by default for space savings and security.
No. You will have to use it to enable some features of JS functionality as well.
devloper.android link:
http://developer.android.com/reference/android/webkit/WebSettings.html#setDomStorageEnabled%28boolean%29/MDN explnation about DOM storage:https://developer.mozilla.org/en-US/docs/Web/Guide/API/DOM/Storage
You need to know there are security attacks that can be made (if you use it with js).
It opens some security vulnerabilities of the system.