Questions about Dumbledore, the greatest wizard in Harry Potter?

1. The memory in the pensieve is his own experience, or obtained from other people's memories.

2.=

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Correction, it should be that his arm was burnt black. This is the result of Voldemort getting rid of dark magic when he got the horcrux. Later, he often looked at his arm and said that he was old.

3. Lao Deng must be dead and can't be in any horcrux. As for why Harry saw him,

I think it has something to do with elder wand and two other hallows.

The fox finally sang an elegy in front of Lao Deng's grave and flew away. Personally, I think he should pursue Dumbledore, because the phoenix will not die, but they may choose to follow him after the master dies.