When you installed WordPress in that subdomain’s subdirectory you created a second discrete WordPress instead of a site on your multisite network. This new site can’t be within your network as it exists outside of that.

Same as if you took any other WordPress site and tried to make it a part of your network – you can’t unless you migrate that site into your network.

It sounds to me like you missed some points in creating your multisite if you don’t have a network dashboard where you would have created the new site.

I’d suggest you hunker down and reread the documentation about building the multisite.

From there you’ll need to add a site. You’ll then use the site’s dashboard from the network dashboard to get to the domain mapping and you’ll need to ensure your domain exists in DNS and points to your server.

And you’ll need to make sure your Control panel points your new domain or subdomain to your root WordPress install which should be in the webroot.

Then you can take the content of that second site you built and migrate its content into the new site on the multisite.

I love multisite but it’s often a real pain to balance all that extra information up in your head while creating and configuring sites. Stick with it though… knowing multisite well puts you into a different group of WordPress developers who have an extra stash of tricks and knowledge.

No, No, and maybe.

The multisite install needs to be in webroot or installed per this document to run as if it was installed in the webroot.

https://codex.wordpress.org/Giving_WordPress_Its_Own_Directory

The webroot install is easiest and I would think that’s where your multisite is.

Your other site is fine where it is if it works with the domain you intended it to work with. You can always migrate it into the multisite later or just start over and create the site within your multisite now.

DNS needs to be setup however you choose to do so and will either be done via the registrar’s facilities or your own on your server and most likely through the control panel. That’s a subject that is outside of our sphere of interest here in WordPress itself but we can try to help guide you.

Your domain name provider or host can also help you with that.

There are two different ways a multisite can be built… subdirectory or subdomain. Makes little difference with the domain mapping capabilities multisite has but will explain some of the oddities in naming the sites.

Let’s us know if you need further help or pointers to other documentation.

There’s some subtleties in each host that can make it fun to figure out but take it step by step.

The multi-site in the root.

The DNS points at the server where WordPress then deals with the site.

Some servers need to be told where to point the domain or else they will send the domain to a second directory on the host.

To me, this is all worth it but some users would find that ‘too much to take in’. That’s cool, too. There’s plenty of ways to build a website.