My Answers

1. A player randomly shoots someone at round start and MPs have detained him.
Talk with the Player asking why he shot the person in the first place, consult with the MP who has detained him and then finally the person who was shot. If I find that the Player who randomly shot someone is guilty of a Marine Law violation to do with misuse of equipment and attempted manslaughter then make sure the MP files it properly and all correct procedures are followed.

2. You see a player walking around the ship naked and clearly lost.
I would first contact them through PMs asking if they need assistance. Providing as much information as possible to them on how to get equipped and possibly give them a basic tutorial if they're that new to the game.

3. A player is being very rude to you in Adminhelps and requesting to speak to an higher ranking staff member.
I'd inform my higher ranking staff member, letting them know of the request of the player, attitude and disrespect towards me. To back this up I'd make sure to take screenshots and copy the logs down for use of the higher admin.

4. You notice a player with a name that doesn't fit our naming rules. The player is arguing that: They've used the name for several years, no one has told them to change it before, and that they didn't know it was a rule.
I'd give them a PM informing them of the rule, and it's the rules of our server and ask that they respect them for that. All servers have different rules! But you should always make sure you have read a servers rules before playing!

5. You see a Maintenance Tech running around in armor and carrying a rifle. The security level is green with no threat present.
I'd note his name and give him a PM. It may be possible that he is RPing some kind of situation and/or was ordered to for whatever reason.

6. The round is stagnating. There are 14 marines and 4 aliens. The marines won't leave the ship, and the aliens won't attack. What would you do, to "encourage" the sides to engage each other?
First off, I'd set myself as one of the admin roles like as an 'Admiral' for the USCMC and I don't know one for the Aliens so I apologize... But for the marines I would motivate them and get them onto the ground "to finish what they started"

7. A marine is running around disarming, punching and stealing gear at round start.
I'd PM them informing them to stop doing so, if continuing I would give a warning then inform an MP.

8. A marine has killed another marine. When you ask him why, he said it was because the other marine had punched him/said something mean.
I would inform him that he has also just broken marine law by murdering a marine. That he was not in the right for punching him but there are MP's to deal with this situation if you informed your squad leader. And give a warning.

9. There are minor racist comments going on IC. 9 of the 10 people are laughing and RPing but one player gets offended and Adminhelps about it.
I'd inform him that I will ask them to stop with the racist comments as other players are getting offended. I will not include names but make sure they persons involved are aware that people are becoming offended with the comments.

10. A marine opens fire at round start in briefing killing multiple marines and instantly logs off.
I'd consult with a higher admin before issuing either a Temp Ban or Perm ban.

11. You see a player playing a xeno larva/chestburster run towards the frontlines and die.
I would PM the player asking if they are/were new to being a Xeno. Then inform them on how to Evolve and play as Xeno properly.

12. You see a xeno memeing, saying AYYLMAO, REEEEEE etc in hivemind chat.
I'd PM said xeno informing them that they need to be serious about the roles, and follow server rules.

13. A Command staff player at briefing near round-start mentions there are aliens on the planet.
I'd PM him saying they the Marines shouldn't know this yet! And that next time in a briefing they should not bring it up!

14. A Marine kills another Marine on the EVAC Pod to take the last spot and claims it was RP as he was saving himself.
I'd look at the chat logs of the Marines, if their chat looks like they were role-playing it, I will personally let it go, Otherwise I would give a warning for it.

15. You see a fellow staff member give wrong information in an Adminhelp or incorrectly enforcing a rule.
I'd PM this Staff member asking about why they gave the wrong information / Incorrectly enforce a rule and then report it to a higher up with screenshots.

16. You see a fellow staff member abusing his powers in-game.
I'd take screenshots immediately and inform a higher admin/staff member.

17. You see a player talking in OOC chat about what he did with your mom last night.
OOC is OOC, They can be as ridiculous as they want in there... As Long as it doesn't get too personnel and people don't get insulted personally. If so, I would then take action. It's alright to have a joke, as long as the joke is seen on both sides...