Second subject in which movement? Both the Minuette and the Rondo have second subjects. And… it’s where the music changes character. Trust your musician’s instincts, look at the music and listen again, and see where the music changes styles a bit

I don’t know why you think the first movement should end in E major or minor. It starts in A, and first movements usually end in the same key they start in

Also, remember composers don’t follow rules when they compose, they follow genre conventions and they can break those at any time if they feel like it. Like the Hallmark Christmas movies that are popular in parts of the world in December: a script writer isn’t going to get in trouble for breaking a law if they don’t follow the standard Hallmark movie tropes. And yet the girl always is coming home to her small town from her job in the big city, and she always has a handsome city guy to break up with and a handsome Small Town dude to fall in love with. The writers don’t have to do that, it’s just the style of the genre. And sometimes some of the movies will break convention in surprising ways

Same thing happens with Mozart and sonatas. He wasn’t following a rule book, he was following genre conventions, and you’ll sometimes find him doing surprising or different things because it’s fun

A sonata and sonata form are different.

You'll have sonata form within a movement of a sonata but not necessarily all the movements. The first movement is a theme and variations