did mozart ever write?

Yeah man, I think they all did!

Yes, that's all he did do, he could improvise with just two notes, that's all you had to give him and in a minute or two he would compose a whole concerto....he was a genius with perfect pitch !!!!!!!! As for composing for others, composers back in his time did write and compose for everyone, women, family, royalty, and especially Kings, and people like Mozart wrote all the music for the court, they were hired for specifically that purpose !!!!!!!!!!