This direct quote from Wikipedia should answer your first question:
The British names go back at least to English renaissance music, and the terms of Latin origin had international currency at that time. Obviously, longa means 'long', and the rest rarely indicate relative shortness. Brave is from Latin bravis, 'short', minim is from minimus, 'very small', and quiver refers to the quivering effect of very fast notes. The elements sem-, dem- and hem- mean 'half' in Latin, French and Greek respectively, while quasi- means 'almost'. The chain semantic shift whereby notes which were originally perceived as short came progressively to be long notes is interesting both linguistically and musically. However, the crotchet is named after the shape of the note, from the Old French for a 'little hook', and it is possible to argue that the same is true of the minim, since the word is also used in palaeography to mean a vertical stroke in mediaeval handwriting.
For the second question, the first thing I found was this:
[the U.S. names] were originally translated from the German names for the notes because so many German composers immigrated to the United States in the 19th century.