You can take videos and photos around the park. What you can and can't do in the shows will be explained before the show starts by the host. As for sending in video, I'm not sure what you mean.
You can send a homemade movie anywhere you want.
The "send in" is a question. You can take videos of the park and rides without using lighting from the device. If you are asking to send videos to Disney then the question is what are you trying to accomplish. There are tons of video blogs out there that will take videos.
You can take video inside the park and no flash photography in the shows. I don't know if you mean send in homemade movies to Hollywood Studios.
It is a Theme Park.
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