Video most definitely works. Don't know about Chromecast, though.
1) yes, that doesn't work;
2) Yep, that's how vm03 programmed it, I think. If you have a suggestion for the action, please don't hesitate to throw idea or two here

3) Data is dropping because of not-so-good network coverage where you are. Wifi drops, you can remedy that by changing timeout of wifi sleep policy. When your phone is locked wifi disconnects to save your battery and connects on intervals to check for any new stuff. I think default value is 180 seconds, and you can lower that, but I suggest leaving it that way or you may suffer severe battery drainage. You have been warned

4) Screenshot should be ok;
5) Apps disappear because you moved them to SD. Move vital apps back to phone. You mught wanna consider repartitioning your internal memory if you lack space.