Okay. IANAL, but software licenses I had to research a lot, so let's see whether I can explain it and if my understanding is correct.
Maybe look at https://tldrlegal.com/license/gnu-affero-general-public-lice... first. The AGPL GNU page https://www.gnu.org/licenses/agpl-3.0.en.html also covers questions and has an explanation. I think the summary covers it already:
> It requires the operator of a network server to provide the source code of the modified version running there to the users of that server. Therefore, public use of a modified version, on a publicly accessible server, gives the public access to the source code of the modified version.
So the license requirement is for the users of the software directly. They need to get access to the modified source.
> So, who does need to be provided with a copy? Just the 'administrators', the people using it to send email?
If that is a closed group said group. If it's the public the public. So in your case yes, the administrators.
You could make the argument (it has been tried before with editors) that the email is part of listmonk, but reasonably it would not stand. At first look there is more weight behind the argument that accessing the email is a form of network access between the user and listmonk, vie email, but I don't think that would hold up either, given the implications with regards of what is a software and what is a product.
> What about if I modify it and repackage it as monklist or whatever, and charge people to use it. I must give them the source code for listmonk too, and, since another requirement is same licence, the source for my modified version?
I don't think that you have to give the original source of listmonk, but you have to give users - including those who access the software on a server, like in a SaaS scenario - access to the source code of monklist, yes.
> i.e. monklist couldn't be closed source, but myapp that happens to use listmonk unmodified for sending emails can be?
There it gets murky. There are different understandings of when a software with different parts becomes one thing and thus the AGPL and GPL apply, and afaik that's not very well tested in court. That said, yes, if myapp just uses listmonk and is not a modified version of listmonk and listmonk is not an integral component of it, then myapp is not influenced at all by the AGPL. AGPL talks about "modified versions of software", myapp would be no such thing.