You will automatically get your desired, password-protected https://[whatever].homeserver.com, pointed to your server. (It's autoconfig too with your router). When you access that remotely, you get access to your WHS server, plus all your connected devices. (it looks something like this: http://www.roughlydrafted.com/RD/RDM.Tech.Q1.07/5B259B0F-B5B...)
For public URL, you can install dropbox on the WHS box or one of the connected PCs, if you'd like.
For movie playback, that's separate from the WHS. You need to think of the WHS as the Server and the playback devices as the Client. In this way, the WHS is very extensible and your playback options are limitless. You can use windows media center on a different PC, or just use VLC or windows media player.
Effectively, WHS is a very "insanely great" home server that stores your files and serves it, allowing you to decide how you want to consume it.
For what it's worth, I use windows media center on a machine connected to the TV, and a logitech dinovo mini for remote (see: http://www.logitech.com/en-us/keyboards/keyboard/devices/384...).
Because I'm a home theater junkie, I did start a side project called http://www.intellimote.com that uses the iPad as a remote to browse and play movies.