First, up through TMP, the US Navy was the model, enough so that, instead of commodore, Kirk was promoted to Rear Admiral, because the navy had changed the name of the rank by that time.
Second, senior officers in the US Navy do not address junior officers as "mister". Depending on the situation, they use surname, rank and surname, or rank. Junior officers and enlisted call officers up through captain "Mister" and surname, except the CO and XO.
Third, the "r" in colonel comes from the Spanish version, coronel. IIRC, "Leftenant" once referred to the lieutenant on the left, and there was also a Rightenant. That would have been back when the officers in an army consisted of the captain, his senior lieutenant, his couple of junior lieutenants, the most junior of which carried the ensign, and was therefore called ensign, and he might have had a sergeant to help with his army of about 20-30 enlisted.
Fourth, Dax calling Sisko "Benjamin" in public or Bones calling Kirk "Jim" in public does go against the professional standards of today's navy, but it happens there, too.
Fifth, Starfleet has never been shown doing anything that hasn't been a standard naval mission updated to the fictional technology and outer space milieu.
Humanitarian, diplomatic, exploration, etc. are all there. Instant communications has reduced the need for a captain to act as an ambassador, the fact that we've already been almost everywhere on Terra reduces exploration, but it's still part of the job.
Sixth, officers call enlisted by surname, rate, or rate and surname, or as the longer form. Enlisted do the same when in official settings, and often in social settings among peers. So I can be petty officer Darkwing, QM1, QM1 Darkwing, or Darkwing. Junior enlisted who don't know me, or who are in trouble will call me petty officer. Same if in a formal situation, such as disciplinary review board, reporting aboard a new command, or requesting permission to come aboard. Among my friends or peers, it'll often be surname, occasionally first name.
Chiefs, though, to officers and enlisted, are Chief/Senior Chief/Master Chief surname, or Chief, Senior, or Master Chief. O'Brien should have been called "Senior", not "Chief".
And "shipmate" is a derogatory term now, instead of the intended meaning. The only way we normally hear it used anymore is to mean "Dirtbag I outrank and intend to publicly humiliate". We joke about the chief's version of AD-OLS: Attention Deficit - oh, look! SHIPMATE!!!!
Now, if the above doesn't soothe any qualms about calling Starfleet a military, the forms of address, and professional conduct, then you're on your own in figuring it out.