1. How many ballpoint pens do you have?
2. How many ballpoints do you have?
3. How many ball pens do you have?
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Is #3 incorrect?
4. It's close to my house.
5. It's near my house.
6. It's by my house.
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Do you use the the expressions frequently? They have the same meaning, right?
No one will know what 2 or 3 mean without context. Sentence 1 is best.
All three of 4, 5, and 6 are commonly used, and yes, they mean the same thing.