American Revolution and Revolutionary War: Was the United States' sovereignty ever officially recognized by Great Britain?

Not until the Treaty of Paris in 1783 formally ended the war. By that time, several other countries had already officially recognized the United States as independent, and Great Britain had afforded de facto recognition when it treated the U.S. as an equal party in the peace negotiations that ended the war. The treaty just made official what had already been decided on the battlefield.
Diplomacy in the American Revolutionary War
At the same time Richard Oswald was asking if the terms of his commission to negotiate with the Americans could be slightly reworded to acknowledge that the 13 so-called colonies referred to themselves as "United States", and about 24 September [1782], the Americans received word that this had been done.

Yes. The Treaty of Paris in 1783 recognised US sovereignty. The Native Americans who had fought on the British side were unhappy that it did not in any way recognise their territorial claims but handed their lands, presumable with them on, straight to the new US. Thereafter, Britain recognised the US as an equal, though got heavy handed in ways that led to the War of 1812.
Can Brazil colonize Portugal?

Not only we could, as we are doing this!Portugal spent a lot of money on Euro 2004. Many Portuguese stadiums became white elephants. Portugal has historically never had a strong economy. It only produces cod, oil, grape, wine and olive oil. Products that do not have much added

What does a communist's home look like on the inside?

Like anyone else's. Maybe the bookshelf contains a bit more communist literature than the usual but that's usually about it.My wife's best friend and her mother are both active communists. You would never guess from anything in their house. They don't festoon their home in red flags or have portraits of Marx and Lenin

What would have happened if Germany had been invaded by all its neighbours in 1938?

They took on France in 1939 & the other powers, Netherlands, Switzerland and Denmark would make little difference. An invasion by Austria would have been unlikely in 1938, given the Nazi inspired coup by Seyss-Inquart against the Fascist government of Dollfuss, but Poland had a much larger army than is generally imagined and in the early 30s