Yes, you need to buy (register) a domain beforehand.
The e-mail provider of your choice that provides custom domains will ask you to

• either point your domain to their nameservers (done from the domain provider’s panel)
• or insert/update some DNS records on your domain (either from your domain provider’s panel if it is supported or you can link your domain to another DNS service e.g. CloudFlare)

Cheers! 😉

This might help you: https://iliasa.eu/wireguard-how-to-access-a-peers-local-network/

No problems at all.
I setup a 3-way folder sync between 3 nodes:

1. Desktop (Linux)
2. Android
3. VPS

VPS is always on, so even if my smartphone is not connected to the internet when I log off of my desktop, the smartphone automatically fetches the updated folder from the VPS .

I haven’t used git for this purpose but I’d think the process would be tedious. Manual commit, push, fetch …

Also, I tried to set it up with Nextcloud but I couldn’t get Android Logseq to use the Nextcloud folder for some reason. I don’t remember the exact issue.

That’s what I use.
Logseq with Syncthing for interoperability between my PC & smartphone.