1. Uncle has made an appointment to see the dentist.
2. Uncle has done an appointment to see the dentist.
I would like to know which is grammatically correct or not.
1 is correct.
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I'm not aware of any variety of English where "uncle" is used like that.
It's either Uncle Pete, Uncle Bill, or Uncle Tom, naming the uncle, or my uncle, your uncle, her uncle, showing whose uncle it is.
The same is true for 'aunt' and 'cousin'.
It's "make an appointment", not "do an appointment".
CJ