The Review
Explain "Random Death Match" and give an example scenario. An example of RDM is when someone randomly kills another player. RDM / Random Death Match is one of the most common rule breaks in DarkRP. RDM would usually be dealt with a warn or if the users RDM's in large numbers then a small to medium ban should be issued. Repeat offences should result in a perma ban.
<-- Not incorrect, however you haven't given the definition of RDM itself. Example provided could be a expanded a bit but it's fine.
Explain "New Life Rule" and give an example scenario. New life rule or NLR is when a user returns to the place of death within the time limit set by the server owner. A example would be when a user is killed and then returns to his place of death before the time limit is up. A NLR break is usually dealt with a simple warning. Repeat offences should result in a small ban.
<-- NLR isn't limited to certain places. Players could be breaking NLR whilst being in a differe t district. Example is okay.
Explain "Metagaming" and give an example scenario. Metagaming is when someone uses in game specifics to reveal information that the player should not know. A example of this if a person saids a user is a theif without actually witnessing them stealing.
<-- This isn't PERP. While the definition itself isn't wrong in general, the metagaming rule is not that serious here. It only reffers to IC info being relayed through appropriate IC channels.
Explain how you would handle the following situation:
Player x accuses player y for RDMing him, the console log shows that player y killed player x.
In this situation I would bring both users to a area which no one was currently present and ask both of them to explain the situation, If there was a proper story behind it I would work out if either party should get a warn or if it was a direct RDM then I will issue player Y with a warning.
<-- You shouldn't warn based on stories. Trust me, sometimes the rulebreakers can make really convincing ones. You should always ask for proof, unles a confession takes place.
Explain how you would handle the following situation:
Player x accuses player y for breaking NLR, the kills are pretty close together in console (a few lines apart) at a peak time.
As there is direct console proof and it is at peak time, to save more time I would issue player Y with a warning without any direct consoltation and then move on to a additional report.
<-- Highly wrong. You shouldn't base your judgement only on logs. What if player Y was spawnkilled or killed player X in legitimate self defense? And you shouldn't warn players without talking to them so they can understand what's wrong.
Explain how you would handle the following situation:
Player x calls for help in the OOC chat because his bank is being raided
Ignore the chat completely as that player should know that it is not valid to call a admin using OOC and that the bank being raded is part of official RP and should not be interfeared by administrators unless there is a breaking of rule(s)
<-- First of all, we don't take OOC requests, we sometimes even mute players constantly spamming the OOC chat. Player X is doing a completely different thing here; consider redoing this part completely.
Verdict
You do have potential, however multiple parts and ways of handling from your applications are wrong. Rules differ from server to server. I suggest reading them over again, and also your activity is bad. You need to prove us that you will remain active

for now.
Good luck.