Can't answer the first one to a standard appropriate for this subreddit, but would suggest that you read his Maxims - he outlines his approach to strategy well there.

Napoleon was lucky with his family. His middle class father made sure to send him to the school in France (Corsica being a French possession) in Autun, and from there he was accepted into the military academy at Brienne-le-Chateau. The fact is that he understood maths well - one observation that because of his grasp of maths, history, and geography 'This boy would make an excellent sailor'.

The art of artillery is basically all maths - trajectory of a cannonball can be calculated by a primary school child with the correct formulae. For this reason, being good at maths makes one a prime candidate for being an artilleryman; and he was admitted to the Ecole Militaire (the Oxford of warfare in France) to train to be an artillery officer. The hardest leap to make in the military is from NCO (rank and file troop) to commissioned officer class, and his theoretical ability (twinned with his father's investments in his education) meant he was good enough to train to be an officer from the off.

This then put him in place to demonstrate his abilities: the folklore is that Napoleon was a poor Corsican, who happened to be in the right place at the right time. And whilst that's partially true, it only really covers his political success. His first major engagement was at Toulon, and he was appointed overall commander thanks to the intervention of Robespierre's brother, with whom Napoleon had developed political ties to through his Corsican nationalism.

He was a leader of men, and being artillery meant he had a far better grasp of the theory of warfare than some of his infantry counterparts - Wellington's attitude to walls was just to send more and more men at them, even when previous attempts had failed. Napoleon, meanwhile, understood that a grand battery of artillery could be more devastating than a mass of infantry, when used correctly, so this became a mainstay of his (exemplified, of course, at Waterloo) - and so his victories tallied up. And with victories comes promotion.

Basically, he rose quickly because he started as an officer, had political connections, and was a competent leader and a brilliant artilleryman.

Allan Mallinson, The Making of the British Army.

Lawrence Freedman, War. Maxims.

Tim Clayton, Waterloo.

Frank McLynn, Napoleon.

Hope that helps!