This declaration is very bad in its actual state...
Points 1, 2, 3, 4 and 5 are fine.
The preamble is way too pedantic... "first in the history of existing humanity Space country Asgardia", really?
Plus, birth is not a right, it's a fact, and the universe does not grant any right to any species.
"We, the free people of the space nation Asgardia, adopt this declaration" would be more than enough.
For the same reason, I would sign with "Asgardia, space state". Even though "space state" is not a notion yet and Asgardia will probably define it, "the space state" is very pretentious and supposes that there will be no other space state.
Point 6 should be rephrased as "Asgardia does not interfere in the affairs of the states on Earth and expects reciprocity". Unless it is meant to mean that if another state interferes in Asgardia's affair then Asgardia feels allowed to interfer in this state's affairs. This is not a good idea.
For the point 7 I do not think Asgardia is meant to interact with the Earth other than to promote space exploration. It should not interfere with Earth politics, earthly state can do that.
Point 8 is ok, but is would be good to have a list of rights before-hand in the declaration, otherwise the second part about "exclusive rights" does no mean anything. I think the Universal Declaration of Human Rights from the UN can be referenced as is in a statement.
Point 9 is a serious bad! It denies freedom of reunion (because that is all a political party really is). And as politics is either the relationship between governement members and its people or with other governements, Asgardia is already engaged in politics.
Points 10 seems overly poetic which removes all clarity. Moreover it adds little information. It should be merged with point 3, which would phrase "Any citizen of Earth, wherever he or she resides, can ..."
Point 11 is phrased in a very weird way, the second part on religion should be removed altogether. Plus Asgardia is not a country as it has no territory, it is a nation or a state (actually nation might not even be right as Asgardians do not form a uniform culture, we have different language, ethnicities and cultures and this diversity should be encouraged).
Point 12 attacks the freedom of information as it can be understood as an prohibition of discussing or teaching Earth history. On top of that it would be stupid for a Nation whose citizens live on Earth to deny the history of the place they live in.
I hope it changes or I'll have to create "Ragnarock, another space nation"