We still have a long way to go towards our goals.

Where can I read about the ongoing projects and apply for work? I'm a dev and I'm interested in developing for our Kingdom.

Also, how can I register a business in Asgardia?

To open business in the Asgardia you will have to wait until the approval of the parliament and the inauguration of the head of the nation in Vienna.
Then the parliament will choose the government, and will begin to approve laws, including those relating to business and the tax system, and the government will implement them.