I'll give a brief answer to the third question, What effect did its closing have on the U.S. economy?

As you probably know, the bank was created with a charter for 20 years, it was created in 1791 and the charter failed to get renewed, so it closed in 1811. There were many small banks at the time, but these banks did not handle the financial problems created by the War of 1812 as well as the First Bank of the United States could have. The banks were not united in some sort of plan to control lending during the war. Banks over issue their currency which exacerbates the inflation, where the First Bank would have been able to limit their lending. Without the First Bank, there really isn't too much regulation for banking. States in New England are the exception though, and they will have stable, specie backed notes while the rest of the country is dealing in rapidly devaluing promissory notes.

Banks, especially those in the mid-Atlantic region, began to have problems paying out the specie, the gold or silver a note was worth, on request. Eventually you could not redeem many of these notes for their specie, so their value was greatly reduced. Banks don't want to have to value each others notes as the face value is much higher than they seem to be worth, so any attempt at national control over banking policy/ transferring money is going to be further hindered.

Being at war and blockaded by the British would have raised prices and caused inflation, but the banks added to those problems.