What is the Japanese word for “counter” and how do I ask questions with it?

Question

How do I ask questions like this? "What is the counter word for umbrellas?"

How do I give answers like this? "The counter word for umbrellas is 本."

Answer 1

"Counter" "counter word" is [助数詞]{じょすうし}, but when you ask and respond to "What is the counter word for XX?" you'd usually say like...

「傘は何で数えますか？」
(lit. Do you count umbrellas with what?)
--「（傘は）『本』で数えます。」

「傘はなんて/どうやって/どのように/どんなふうに/どういうふうに数えますか？」
(lit. How do you count umbrellas?)
--「（傘は）『一本、二本』と数えます。」

「傘の数え方は？」 (informal)
(lit. The way of counting umbrellas is?)
--「（傘の数え方は、）『一本、二本』です。」

(You could ask 傘の助数詞は何ですか？ lit. "What's the counter word of umbrellas?", but it's not very common to use the term 助数詞 in daily/normal conversation...)

Answer 2

The term people would use in ordinary conversation is [単位]{たんい｝ (unit of measurement).

傘は何という単位で数えますか。