Louisiana Purchase Treaty: Questions

What would the United States be like today if the Louisiana Purchase had never happened? Other than smaller, obvi.
The only mention of the Native Americans living in the Louisiana Territory at the time is in Article VI of the treaty document. What did the Louisiana Purchase mean for them? What deals did the various tribes have going with Spain when this treaty was enacted?
How did the huge territory of Louisiana come to be divided up into the various states we know and love today? What were the rules? Did people just make up boundaries and towns and stuff, or what?
What did the Louisiana Purchase have to do with Lewis and Clark's 1804 expedition, if anything? Would their little backpacking trip have happened without the purchase? Why or why not?
What is the deal with the intensely specific financial terms laid out in the first convention? Why couldn't the United States just give France a check for the whole $15 million and be done with it before France changed its mind?
It took a little while for the signed purchase documents to make their way to President Jefferson's desk. How did he feel about it when he saw what Livingston and Monroe had done? How did Congress feel? How might the average American have felt?