Is the Stack Exchange engine available?
Is it possible (or planned) to sell stack overflow as a service, so we can create Q&A for our own site, maybe link it to our own domain, and benefit using such a great platform?
No, that is not planned.
A long time ago, the Stack Exchange engine was licensed, resulting in what is now known as the "Stack Exchange 1.0" network of sites. That didn't go so well and the program was canceled.
In its stead, the "Stack Exchange 2.0" program was announced. Run from the Area 51, this allows users to propose new Q&A sites on a particular topic that should be added to the network. The new ideas are proposed, discussed, and built on the Area 51 site. The sites that have built up a critical mass of support and appear most likely to be successful will be launched in "beta".
If you think there is a need for a new Q&A site in the Stack Exchange network, you should propose it on Area 51 and get your friends to support it!
For further reading, check out this blog post by Joel Spolsky, which documents the changes made to SE network as it transitioned from the SE 1.0 model to the current SE 2.0 model.
However, there is a number of clones available, some of which have become pretty mature.