Is unity 3 free to use for unlimited time or do you have to pay for it?
Unity is free. However, some features are considered to be Professional-level features and thus require licensing the 'Pro' Version which costs money. In addition, if you wish to publish to iPhone, it has its own licensing restriction. Unity also offers a 30 day free trial of Unity Pro.
For a comparison of the free and the pro version, look here: http://unity3d.com/unity/licenses