Not to worry. That was just the "art style" of that era. Leaders were often depicted as "in the company" of various divinities and personified virtues.
Yep. Probably romanticism--which as a style of art was still popular in the 1860's (when it was painted).
Brumidi painted the frescoes and used works in the Vatican (Michelangelo and Raphael, to name a couple) as his inspiration.
As a whole, artwork created during that time has several different characteristics (this is by no means an exhaustive list):
-Nationalism and national origin. (hence Washington in heaven)
-Forces of nature, often depicting the raw power of nature
-Human instinct
-Unlike strict neoclassicism (which centered on realism and based in part on Greek and Roman art, mythology, history, etc.), romanticism often took on a view of Renaissance and early Baroque art.
-Emotional, rather than "of the mind"