Answer: If we take certain benchmark tests - yes, it does. In real-life performance, though, it won't be four times faster. You can find more details here.
Answer: If a higher-resolution screen, faster GPU, better camera and LTE connectivity aren't that important for you — or aren't must-have features for you at this point — then it's absolutely not worth the upgrade from the iPad 2. In fact, if you don't care for the above-mentioned features, and aren't using many graphically- or processor-intensive apps, it's not even worth upgrading from the original iPad. In any other case, though, we think there are plenty of reasons to upgrade to the new iPad.
Answer: We wouldn't say that black bars ruin the experience. The screen is still beautiful and bright, and as long as there are some cool titles to watch, we think you're in for a great movie-watching experience. However, if the only thing that you intend to do on a tablet is to watch movies (or if movie-watching is the main thing you purchase a tablet for), then a high-class widescreen Android-based device would be a better fit.
Answer: Absolutely! The new iPad delivers a visibly better performance in graphically-intensive 3D games and apps, compared to the iPad 2. Application start and load times will depend on the app itself. In simpler titles, start and load times are about the same. With more complex ones, the new iPad often has an edge due to its faster processor and more RAM, although the difference isn't that big (at least with the current titles).
Answer: In case you're used to having a great number of installed applications on your iPad, it might be wise to consider a 32GB one. There isn't a rule letting us calculate the size of the Retina-optimized version of each app, and it really depends on the type of app. If it's an application with a lot of graphics or video, you might observe a significant boost in its size, once it gets optimized for the higher-resolution screen. We expect the same thing to happen with magazines. Still, if you don't keep too much stuff installed at the same time, a 16GB iPad might still get the job done.
I am interested in the battery life. I know the new one is like 70% bigger or something (2500mAh I think) but does using the device at full throttle last the promised amount?
Answer: Yes, it does Flash... Kidding. :) You should keep in mind that battery life greatly depends on your usage pattern. If you play a lot of 3D games for a long time, it probably won't last a whole day. However, in most cases the new iPad delivers a battery life that's very similar to what you can get from the iPad 2. In short, yes - it does work as advertised.
Answer: If you are referring to "white" as the color of the device itself - there isn't a difference. If you are asking about the white color of the display - yeah, the new iPad has a slightly warmer color reproduction, which isn't a bad thing in this case, because it's not too much.