I don't have the Hero 3+ but you can measure it with the help of a front picture of the cam and the dimensions of the camera.
Taking the dimensions from here: http://www.dpreview.com/articles/8137555963/hands-on-with-The-gopro-hero-3-black-edition
(5.8 x 3.9 x 2 cm)
And using this picture:
And measure how big the lens casing is compared to the size of the ...
This depends entirely on who you are delivering to. Different broadcasters have different requirements. Most have a delivery spec sheet that you can request, or that they publish online. e.g. here's the BBC one.
This is a document from the ITU :
that specifies Digital interfaces for HDTV studio signals.
This kind of signal is commonly carried on an HD-SDI physical layer.
On a side note, I believe the power is required for the analog to digital converter in wireless transmissions, and not the signal itself, since there is +5V DC power running through one of the pins. So you might actually have better luck searching for USB powered signal converters, because once the signal is digital, you're home free.
Something like this:
Depends on the look you're after. Searching For Sugar Man won the 2013 BAFTA Award for Best Documentary, and it was partially shot on an iPhone, the Blair witch Project used a lot of DV video (standard definition heavy compression) and parts of Natural Born Killers were shot on super-8.
If the content is worth it, or if the style of story telling motivates ...