Not all docker-compose files are development, although it is in this case. The documentation, if available, will tell you what each env var does.
You know the docker-compose.yml will have everything you need though, you just need to tweak it. Absolutely nothing wrong with seeking out the docker-compose as most env variables are self explanatory.
Did you set the environment variables for the database and what not?
When you get stuck like this, always look at the docker-compose.yml file if provided. You can find this one here: https://github.com/mealie-recipes/mealie/blob/mealie-next/docker/docker-compose.yml
It lists all the environment variables that need to be set.
Alternatively you should be able to use docker compose in WSL, it'll still show up in Docker Desktop.
I would do the ethical thing and explain the privacy implications of you hosting it but him hosting it too. Honestly I'd turn on end to end encryption.
You having their data and him having his family's data is a big responsibility. You need adequate security both online and physically.
There's also the fact that he has access to it if he's an admin. Not everyone can handle that responsibility.
As to your original question, Nextcloud breaks often, relative to how often the server will have problems. You'd def need SSH access.
It would probably be better for you to get an ASUSTOR NAS in terms of hardware. It Supports apps and Nextcloud is one of them.
It also has support other than you, which depending on a few factors (magic 8 ball), might be more time consuming than you'd think. They may not want to deal with hardware either if something did occur.
From your diagram you should be able to access it already. It's what is called dual NAT where a router is behind a router.
Otherwise you could turn off DHCP on one and use static IPs / routes
Would it be possible to plug your media server into both routers?
ThePirateBay, the most notorious site in the world, uses Cloudflare. This isn't China. Wiretapping is illegal in most circumstances, and that's essentially what it would be doing.