1. He took a picture of the mountain.

Question

1-1. He took two picture of the mountain.

2. He took pictures of the mountain.
3. He took many pictures of the mountain.

4. Will you take a picture of us?
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Q1: Are they all grammatical?
Q2: Does #1 mean that he took only one picture of the mountain?
Q3: Does #4 mean that the speaker wants somebody to take a single picture of them?

Answer 1

Q1) No. 1-1 should read: Het took two pictures of the mountain. The rest are grammatically correct
Q2) yes
Q3) yes

Answer 2

I think Anonymous means "He took ... " instead of "Het took ... "

Otherwise, Anonymous is correct.