1. He took a picture of the mountain.
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?
Q1) No. 1-1 should read: Het took two pictures of the mountain. The rest are grammatically correct
Q2) yes
Q3) yes
I think Anonymous means "He took ... " instead of "Het took ... "
Otherwise, Anonymous is correct.
Q1: Are they all grammatical?
A1: Yes, all the sentences are grammatically correct.
Q2: Does #1 mean that he took only one picture of the mountain?
A2: Yes, in sentence #1, "He took a picture of the mountain," it implies that he took one picture of the mountain.
Q3: Does #4 mean that the speaker wants somebody to take a single picture of them?
A3: Yes, in sentence #4, "Will you take a picture of us?" the speaker is asking someone to take a single picture of them.