My question is how long is the range from the phone to the ANT+ device. What is the suitable range between ANT+ device? I have seen this demo and I am curious if it is worth my money.
Hard to say the exact range. There is plenty for your standard usage scenarios with standard ANT+ sensors. e.g. phone mounted on bike or in jersey pocket picks up bike sensors while riding no trouble.
Testing my app IpBike with USB ANT stick emulating the sensors and the app running on an Xperia Active I can wander around the same room with no loss of reception. To test loss of reception cases down the garden 10m through the window is not enough to totally lose reception but it is getting patchy. I have to go around to the front of the house and get a good number of walls between the phone and the ANT stick for a total loss of reception.