The emperor was the ruler of the Roman empire. He ruled over many countries and provinces.
# I have brought him to you, especially to you, King Agrippa
"I have brought Paul to all of you, but especially to you, King Agrippa."
# so that I might have something more to write
"so that I will have something else to write" or "so that I will know what I should write"
# it seems unreasonable for me to send a prisoner and to not also state
The negative words "unreasonable" and "to not" can be stated in positive form. AT: "it seems reasonable to me that if I send a prisoner then I should also state" (See: [[rc://en/ta/man/translate/figs-doublenegatives]])
# the charges against him
Possible meanings are 1) the accusations that the Jewish leaders have brought against him or 2) the charges under Roman law that apply to Paul's case.