It does have some internal storage capability but cant remember what the number is now. I watch Netflix, Amazon Prime, Hulu Plus and HBO go. and never had a problem. I was told one the internal storage was mainly for the gaming feature.
Make sure you get the 2015 model. there are still older ones out there and cant hold a candle to the new one. Says 2015 on the box.
If you want to see the full spec. try the review at CNET. just type in Roku 2 in to your search eng. and look for the CNET review. there is also a comparison chart there of all the streaming devices. Kim Komando also has a comparison chart at here web site. komando.com

The only difference is the remote. the Roku 3 ($99) come with a romote that you can speak into and fine the movies/shows you want. It also has a headset that attached to the remote. If you don't think you will use these features save the money and get the Roku 2. have a friend who got the 3 and the voice thing was fun for awhile but he no longer uses it. He never used the headset.

yes you simply log on with the same user Id and password. I use this system on the living room and bedroom tv.

The roku like all steaming devices uses WiFi. so you must have an internet connection