How to control computer from iphone without anyone seeing what you are doing?

I basically just want to be able to have my iPhone 5S with me from one room and my computer on from another and be able to watch things FROM my computer like movies, Youtube, etc. HOWEVER, I do not want anyone to know that I'm actually doing anything, so I wish for the screen on my computer to be blocked from view (like a black screen) as I'm doing so. Is there any program that allows me to do this?

What can I do to fix my iPhone? - 1

I tried to update my iPhone to the latest iOS but it shut off and now is stuck at "Connect to iTunes." It says on my computer that I should try to restore the phone but i don't want it to delete all my apps and i don't know if the phone is backed up or not to get it back. When I tried to restore it, it says there's an error with connection when the connection is fine. I can't even use my phone right now. It won't turn on and its stuck at Connect to Itunes.

Regardimg charging iphone through laptop via USB cable?

This is my issue. When I start my laptop (running Windows Vista), when I plug in my iPhone through USB, I can charge it and access it through iTunes as it should be but as soon as I unplug it, when I replug it the laptop doesn't recognize it and it won't charge at all. When I access device manager, I see a little triangle with an exclamation mark saying error code 10. Any idea how I can fix this issue?

Why is my iPhone stuck on Connect to Itunes?

I tried to update my iPhone to the newest iOS but it shut off and now it is stuck at connect to iTunes. It says on my computer that i should restore the phone but i do not want all my apps deleted and i don't know if my phone is backed up to get it back or not. What should I do?

Do I need a TV to use a ChromeCast?

I want to use a chromecast straight to my projector (acer x112) unfortunately it doesn't have a HDMI port. I have an Xbox 360 that links to my projector through a VGA however it does not have Xbox Live so I can't receive Iplayer ect. Is there any way of using a ChromeCast without having a TV? For example, could i plug it into my Xbox 360 and stream programmes from my Iphone on to my projector screen through the Xbox without ever coming into contact with a tv?
Cheers