The first sword is what is generally referred to as a Ketland, but that in no way indicates it was made by the Ketland firm. This style was copied and used by many British, US, and German makers. If I had to guess, I would say it was a Birmingham product, probably from the early 1820s, although the plain stirup hilt might suggest a somewhat earlier date.
The second sword is the UK P1796 light cavalry saber which was also widely copied, e.g. the Prussian M1811 Blucher saber. A lot of similar style sabers were used by American militia elements, but I would be suspicious of any marked "U.S.". I'm not aware of any saber with ears on the grip with genuine "U.S." markings, but I've seen a number with the markings applied in modern times in an attempt to enhance their marketability.