Louisiana Purchase: cheap but globally lucrative?

The period around the rise of Napoleon and the war of 1812 is confusing. Supposedly, both Britain and France were fighting to stop the US from trading with the other because they were at war. The French monarchy had been overthrown in the 1890s and slavery was abolished in France shortly thereafter.

Napoleon rose to power through the ranks of the military, effectuated the sale of Louisiana to the US for relatively little money, and a year later re-established slavery. Was the Louisiana sale cheap because it was intended to facilitate expansion of colonialism into the US interior? Was slaving and capitalist business in New Orleans and along the Mississippi river lucrative enough to warrant selling the huge amount of land purchased with Louisiana for colonial gain?

Further, why were the British interested in fighting for New Orleans in the battle of New Orleans? Was it to secure trade-route control and thus make more money off colonial trade? Was it to control slaving to either profit from it or abolish it and establish wage-labor capitalism as a more lucrative system of colonial exploitation?

France/Napoleon supposedly only re-established slavery to re-establish order in the colonies. Does that mean they actually had other economic plans that were oriented toward phasing out slavery, or were they just finding out that they weren't doing as well economically as they would like without slavery, so they were re-instituting it in hopes of securing greater economic gain than with a republic?

Also, what was the relationship between the US and the British empire with regard to slavery? Andrew Jackson was the general who fought the British at the battle of New Orleans, but later the British supported the Confederate southern states in maintaining slavery. Free slaves and American tribal people supposedly fought on both sides of the battle of New Orleans, so it is unclear what if any political-economic differences were at stake. I.e. were slavery and colonialism moving in different directions among the US, French, and British; or was there just fighting over who would control economic resources and trade routes, including the slave trade/routes and the spoils of slave labor?