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.
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?)
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.
Anonymous is correct.
Your first four sentences are all fine; you should not leave "best" out; it needs to be there.