Can you say?

1 Is this meat cooked enough?

and do you say:

1 Her palate is high arched/Highly arched.

"Is this meat cooked enough?" is fine.

You can also say "Is this done enough" or "Is this too rare?"

I don't understand your second question.

In over half a century of speaking English I have never had the need to compare the palates of females.

I can't ever imagine myself saying such a sentence. Perhaps someone in the medical profession might need to make some comment about this.

Her palate is curved more than one would usually expect - is one possibilty.
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Number 2

The palate of her mouth is highly arched/arched highly
meaning it has an unusually curvatuous.

Which would you say?
Thank you
 Optilang's reply was promoted to an answer.
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GG's answer to your first question is perfect.

In the second sentence, I too am puzzled as to what you mean.

If you are trying to say that she is a gourmet with a highly educated palate, for example in judging wines, the word 'arched' is not correct. You could say she has a 'sensitive' or 'exceptional' palate.

If you are referring to the physical palate at the back of her throat, you would say that it is highly arched.

Hope this helps,