I have two threads going here you should read...
Primary Objective – Hovering, not Maneuvering
In multirotor, hovering is maneuvering, it takes a fast electronics at high refresh rates to keep a quad stable in a hover. Those same characteristics make them maneuverable.
Dimensions – More or less the palm of your hand
Good luck with that, there are plenty of small quads and its but nothing that would carry the load you wish. You are looking at a 550 or 650 size quad frame and above.
Maximum Possible Altitude of Operation – 3000 ft
This is easy and I do this myself, but it requires UHF long range control systems and good video with the antenna turned 90' as to get rid of the null zone which usually points straight down.
Operation Time – Anything above 5 minutes would be good. 10 minutes would be great.
I get about 6 to 8 minutes and I hope to get 10 with a 3300 4 cell, but this is on a 650 size quad, take a look at my videos to see what it's capability is.
Weight – The less the better, but that not a main concern.
It should be one of your biggest concerns, weight = flight time.
Price – The same.
I could build this for you without HD video feed (because none exists) for about 3 grand turn-key with transmitter.
On board HD video capture and transmission in realtime. Audio is not required.
You will not get HD video transmission, the hardware, if it exists is not available to hobbyists. The best you can hope for is to record HD video on the aircraft using a GoPro or similar camera, I personally use a Contour HD camera but I also record my video feed in case I crash, it helps find the craft and the OSD displays GPD cords on the screen to aid in finding it at such long ranges beyond line of sight.
Data transmission in real time (altitude, attitude, battery level, additional user data)
This is easy and it's called an OSD (on screen display) usually getting all it's data and calculating it from a GPS radio.
Pre-Programmable and Remote Control Capabilities
If you mean way-points, then tack on another $600 to the price tag. Mine will come home and land in the events of lost signal or by the flip of a switch, but to fly way-points per-programmed on a map or laptop is another league altogether.
The more hardy and durable (less fragile and gentle) the better
I can help with this as well, but inherently multirotor craft are not very durable, they have exposed props and they break a lot, the frame arms and landing gear also break. Expect them to break in mishaps and have spares available.
Optional large-distnace communication is good
My current record is 2km, out and back, but I have spent a very long time and lot of money, are you prepared to do the same?