My understanding of Microsoft implementation of whats going on in the cloud is very complex and are large sums of data, processed and what is sent to the Xbox One are only small files (KB). At this point what they are doing with cloud processing the speed of your internet won't matter. But as the life cycle progresses years down the road and they try to use the cloud to push "the power of the Xbox" the data packs I'm sure will get much larger(MB's) and the games will become "always online". The quality of your internet connection will become critical.
Launch titles like Forza 5 you can play offline, but as soon as you connect to the internet it sends your Drivetar info it collected during that 24 hour period to the cloud and then updates Drivetar profiles onto your console.
I'm pretty sure you are correct about being able to connect the Xbox 360 along with a PC or a set top box to the HDMI IN port on the Xbox One.
