What is the purpose regarding this topic? Would you like one of us to tell you what all of the following sentences mean?
What does recent mean?
Recent is used as a decent week.
What does corrupt mean?
Corrupt can be a police shooting a citizen for no reason.
What does 'Abusing your Powers' mean?
Abusing powers is to use noclip to raid, slay someone to raid their shop etc.
What does Administrate mean?
To adminstrate means to take care of f1's and to keep the server clean.
What does Super Administrator mean?
Super admin is the ones that keeps an eye on admins and below, making sure that the server is running smoothly, and doing f1's.
When should all administrators support their community?
Not sure i am getting your question right, but in cases like Distributed Denial of Service as in Denial of Service Attack we'll do anything to stop it. Besides every adminstrator has a diffrent view of certain situations.
When should the ban hammer / demote be used to get out of a situation that may take more time than a usual case?
Do you mean demoting a moderator to user etc, or demoting someone from their job? In user cases, a propspammer should get permanently banned instantly, it's showing nothing but a player who dosen't care about the server. In a situation like a rdming mutant, a demote from the job would fit better.
What does Community Manager mean?
The Community Manager is the one hosting the meetings.
What does 'Acting as Professional Staff' mean?
To act mature, keep calm in every situation and be patient.
Again i don't get the purpose of this, so if this was your question, here's the answer. 
DarkRP 1 
Discord