It stands for numero (ablative of Latin numerus), meaning "in number", "to the number of", "with the number", etc. Obviously it's treated as a nominative in English and pluralized accordingly: "Nos", "nos"

I've no idea why it was written with a capital, but AFAIK the rule is no longer universally observed anyway. I usually write no., nos.

No.

(That's the answer to you second question.)

It's short for 'numero'. There's no need for a capital. Strictly speaking, in BE usage it shouldn't have a dot after it either (but it nearly always does).

Good point. I hereby rescind the rogue dot after "no." in #1.

Thanks folks! Just one of the many things I was taught incorrectly... another example is "Look to the right before crossing the road." - doesn't seem to work very well in Germany...

#2
I wouldn't say a "rule" proposed by Fowler that is widely, but not universally, followed in Britain for some words (like "Mr") but not for others (like "edn." and "No.") means that the dot should necessarily be omitted.

@ 4, wenn Du's bis zur Mitte der Fahrbahn geschafft hast, schon!