1. A flower shop is a shop where people buy flowers.

2. A flower shop is a shop where people buy a flower.

3. A flower shop is a shop that people buy flowers.

4. A flower shop is a shop people buy flowers.

5. A flower shop is a shop people buy some flowers.
------------------------
#1 is correct. What about the others? In the exam, are they regarded as correct answers or not?

I think 2 is correct as well. But the others seem off.

Right. 1 and 2 are correct, but the others are not.

3 would be correct if you replace "that" with "in which" but 4 and 5 are simply run on sentences.
http://en.wikipedia.org/wiki/Run-on_sentence

6. A flower shop is a shop where people buy the flower.

(What about this one? 'The' is used in this sentence before 'flower'.)

Out of the provided options, only #1 is considered grammatically correct.

Let's break down each sentence and understand why:

1. "A flower shop is a shop where people buy flowers." - This sentence is grammatically correct as it clearly states that a flower shop is a place where people purchase flowers.

2. "A flower shop is a shop where people buy a flower." - This sentence is slightly incorrect because it uses the indefinite article "a" before "flower," implying that people only buy one flower in a flower shop. However, this is not what is typically meant by a flower shop, as people generally buy multiple flowers.

3. "A flower shop is a shop that people buy flowers." - This sentence is missing the preposition "where" before "people buy flowers," making it grammatically incorrect. Adding the preposition "where" (similar to sentence #1) would make it correct.

4. "A flower shop is a shop people buy flowers." - This sentence is missing the word "that" between "shop" and "people buy flowers." Adding the word "that" (similar to sentence #3) would make it grammatically correct.

5. "A flower shop is a shop people buy some flowers." - This sentence is missing the preposition "where" before "people buy some flowers," like sentence #3. Additionally, the word "some" is unnecessary, as it is implied that people may buy more than one flower in a flower shop.

In an exam or formal writing, options #2, #3, #4, and #5 would likely be considered incorrect due to their grammar errors. The most accurate and grammatically correct statement would be option #1.