Gramatically, yes on both counts, but listen to the sound of it and go with that.
"in a second" means quickly. He had lunch in a hurry.
Please say hello to your parents.
Give my best wishes to your parents.
Give my regards to your parents.
Give my best regards to your parents.
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1. Are they all the same? Can we add or delete 'best'?
2. He had lunch in a second.
(What is the meaning of 'in a second'? What English word can we use instead of that?)
2 answers
Anonymous is correct.
Your first four sentences are all fine; you should not leave "best" out; it needs to be there.
Your first four sentences are all fine; you should not leave "best" out; it needs to be there.