"I have his number" (or "I've got his number") is also an idiomic way to say "I know his weakness" or "I can beat him." Query whether this sense exists in Polish as well.
Nope, it does not. It's most probably the telephone number, alternatively some other number connected with him, but still - literally a number.
Nice to see you too! You're welcome and thank you so much for the lingot!
I'd use to say, for example
"What's your warranty number?"-"Jaki jest Twój numer gwarancji?"
"What's your shoe size?"-"Jaki jest Twój numer buta?" you can also say "Jaki jest Twój rozmiar buta?" (rozmiar=size) :)
Liczba sounds more "mathematical" ;D to me or maybe statistical like "Jaka jest liczba dzieci w tej gminie?"-"What's the number of children in this municipality?"