1. She won't listen to my advice.

2. She will not listen to my advice.

3. The door won't open.
4. The door will not open.
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Is each pair the same?
Does #1 mean volitional future?
Does #2 mean volitional future or simple future?

Each pair is the same, yes.

They are both in simple future; the only difference is that one is phrased with a contraction (won't) and the other is spelled out (will not).