Not when they are signatories of treaties that define international air travel like the Warsaw Convention of 1929, the Chicago Convention of 1944, the 1955 Hague amendments to the Warsaw Convention, the 1971 Guatemala, City revisions of the Warsaw Convention, and the 1999 Montreal Convention.
The First Freedom of the Air is to overfly a country without landing in it. There are lots of overflights of countries all over the world. Even when the US did not recognize the Cuban government, flights between Canada and Cuba overflew the US just about every day.
Right. Treaties between sovereign states. And each sovereign state can choose whether to enter into or leave a treaty. Or to suspend it. And it can be heavily regulated with permissions granted and denied. Do we remember all the issues with opening up flights over the Soviet Union? (It is true that closing its airspace to the UK would be a bizarre and self-defeating move for an Irish government and would in fact never happen.) (And it is also true that the Irish leader is anti-Catholic twerp.)