1. All the documentation I see is C#? I assume C# plugins aren't going to work on a Linux server? Is this right and/or is there documentation on hooks in other languages?

2. Before I spend a lot of time, Is this possible in Oxide? The first three sound like existing hooks would make it easy, not sure about the last two.
- Limit TCs to one player
- Prevent codelocks
- Prevent bagging another player.
- Log loot transfer between players (e.g. playerA drops a rocket on the ground and playerB picks it up)
- Log all kills, with damage done, by who, and proximity of players

alright so i am a noob developer aswell but i can answer atleast 2 questions for you.

1. for coding language, it doesnt matter on which operating system you execute it on. However, Rust is made in the Game Engine Unity. where C# is the most common used Coding Language.

2.1 = You can check if the TC has a player autorized on it. using the hook:  "object OnCupboardAuthorize(BuildingPrivlidge privilege, BasePlayer player)"

its not much but i hope i could atleast give a decent answer