1. When you are not at home, who takes care of the children?

2. When you are not at home, who is taking care of the children?

3. When you are not at home, who will take care of the children?
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Which ones are correct and common?
Does #2 mean #3?
Can we use 'while' instead of 'when' to have the same meaning?

1 and 3 are closest in meaning, but really, all three mean about the same thing. And yes, in these sentences, "when" and "while" would mean the same thing.

All three sentences are correct and commonly used. However, there are slight differences in meaning and usage.

1. "When you are not at home, who takes care of the children?" This sentence is in present tense and implies a general or habitual action. It suggests that someone regularly takes care of the children when the person being addressed is not at home.

2. "When you are not at home, who is taking care of the children?" This sentence is in present continuous tense. It implies an action happening in the present moment or a temporary situation. It suggests that, at the time of speaking, someone is actively taking care of the children.

3. "When you are not at home, who will take care of the children?" This sentence is in future tense. It implies a future action, suggesting that someone will take care of the children when the person being addressed is not at home.

The meanings of sentences #2 and #3 are slightly different. Sentence #2 implies a current situation, while sentence #3 implies a future situation. So, they are not exactly the same.

Regarding your question about using "while" instead of "when," yes, you can use "while" to convey the same meaning. For example, you can say: "While you are not at home, who takes care of the children?" or "While you are not at home, who will take care of the children?"