I have another question related to the war of 1812, how badly was the white house damaged and what other important buildings if any in the capital were damaged or destroyed during the raid?
America was actually very divided going into the War of 1812. The merchant Northern states didn't want to upset relationships with Britain whereas the warhawks, primarily from the South and West, were for it.
How widespread was coverage of the war? What do you mean by coverage? News-wise, it took weeks to months to get word around. Wars were fought very locally.
I don't know the specifics about DC being burned, but ultimately the war did help shape American nationalism. In fact, it soared afterwards because it gave Americans a sense of true independence. The treaty helped end a lot of British policies towards America that were very unfair, such as seizure of our sailors and ships.