Selfhosted

Look, this is a large puzzle you're trying to solve all at once. I'll try to answer at least some of it. I'd advise you take these things step by step. DM me if you need some more help, I may have time to help you figure things out.

I paid for and installed mullvad (app) but it crashes a lot (for over a minute every 20 seconds), so it looks like I need to configure something like gluetun to do it instead.

Check the error logs and see what's wrong with it instead. How is it crashing? Did you check stdout and stderr (use docker attach or check the compose logs)?

If I want to watch them on my TV I need to connect something to my TV that talks to the raspberry pi, so I have an NVIDIA shield with Jellyfin installed on it - but in order for the NVIDIA-Jellyfin to connect to the RaspberryPi-Jellyfin it needs to go through the internet (if this is not the case, how does one point the NVIDIA-Jellyfin at the Raspberry Pi jellyfin?)

Technically not. You can use the Jellyfin web UI to stream directly from the RPi. You may need the shield if the RPi does not have enough resources for streaming, but I'd try it out first. Try to get the IP the Raspberry is listening on on your local network and put that in a web browser on a computer first. IF you get the web UI and can watch stuff, then try a web browser on your TV, or cast your computer to the TV or something. As long as you have a web browser you should be fine.

First of all, is that all correct or have I misunderstood something?

You should look a bit into how the internet, DNS and IP addresses work on the public internet and private networks. You can absolutely set it up so that traffic from your local network hitting your domain never leaves your home, while if you try the same from somewhere else, you get an encrypted connection to your home. You're a bit all over the place with these terms so it's hard to give you a straight answer.

How does mysubdomain.mydomain.com know it’s me and not some random or bot?

If the question is whether how the domain routes to your IP, look up how DNS works. If you are asking how to make sure you can access your domain while others can't look up the topic of authentication (basically anything from a username/password to a VPN and network rules).

How do I tell Cloudflare to switch from web:443 to local:443 (assuming I’ve understood this correctly)

If I remember correctly, Cloudflare forwards HTTP/S traffic only, so don't worry about the ports, that's all it will do. About the domains, you need to have a fixed public IP address for that, and you have to give Cloudflare by setting a DNS A record for an IPv4 address and/or an AAAA record for an IPv6 address.

So something like this: A myhost.mydomain.com 123.234.312.45

Is this step “port forwarding” or “opening ports” or “exposing ports” or either or both?

Nope. Port forwarding is making sure that your router knows what machine should answer when something on the Internet comes knocking. So if the RPi port 8096 is "forwarded" to the router, then if something from the internet connects to the router's 8096 port, it will get to your RPi instead of something else. Opening ports has to deal with firewalls. Firewalls drop all connections on all ports that are not open, for security reasons. By opening a port you are telling the firewall what entities outside your device can connect to a service like Jellyfin listening on that port. Exposing ports is Docker terminology, it is the same as port forwarding except instead of "moving" a port from your machine to your router you "move" a port from a container to your machine.

If my browser when accessing mysubdomain.mydomain.com is always going to port 80/443, does it need to be told it’s going to talk to cloudflare - if so how? - and does cloudflare need to be told it’s going to talk to NGINX on my local machine - if so how?

The DNS server you are hosting the domain from will propagate that info through the DNS network. Look up how DNS works for more info. If your domain is managed by Cloudflare, it should "just work". Cloudflare knows it talks to your router by you setting up a DNS record in their UI that points to your router, where your RPi's port should be forwarded, which directs traffic to your RPi, on which your NGINX should be listening and directing traffic to your services.

How do I tell NGINX to switch from local:443 to local:8096 (assuming I’ve understood this correctly)

Look up NGINX virtual servers and config file syntax. You need to configure a virtual server listening on 443 with a proxy_pass block to 8096.

Is there a difference between an SSL cert and a public and private key - are they three things, two things or one thing?

Yes, SSL certs are the "public keys" of an X509 pair, while what you know as "public and private keys" are RSA or ED25519 key pairs. The former is usually used to make sure that the server you are accessing is indeed who it claims to be and not a fake copy, it's what drives HTTPS and the little lock icon in your browser. RSA or ED25519 keys are used for authentication as in instead of a username and password, you give a public key to a service, then you can use a private key to encrypt a message to auth yourself. One service you might know that it uses it is SSH.

Doesn’t a VPN add an extra step of fuckery to this and how do I tell the VPN to allow all this traffic switching without blocking it and without showing the world what I’m doing?

A VPN like Mullvad is used for your outgoing traffic. All traffic is encrypted, the reason you want a VPN is not so that others can't see your messages, it's so that your ISP and the other people forwarding your messages don't know who you're talking to (they'll only know you're talking to your VPN), and so that the people you're talking to don't know who you are (they are talking to your VPN). You need this so your ISP doesn't see you going to pirate sites, and so that other pirates, and copyright trolls acting as pirates don't know who you are when you talk to them and exchange files using torrents.

Gluetun just looks like a text document to me (compose.yml) - how do I know it’s actually protecting me?

I don't know shit about Gluetun, sorry.

From https://nginxproxymanager.com/ : "Add port forwarding for port 80 and 443 to the server hosting this project. I assume this means to tell NGINX that traffic is coming in on port 80 and 443 and it should take that traffic and send it to 8096 (Jellyfin) and 5000 (ombi) - but how?

Again, look up virtual servers in NGINX configuration. You need a virtual server listening on 80 and 443 proxying traffic to 8096 and 5000, separating on hostnames I guess.

Also from that site: “Configure your domain name details to point to your home, either with a static ip or a service like DuckDNS or Amazon Route53” - I assume this is what Cloudflare is for instead of Duck or Amazon? I also assume it means "tell Cloudflare to take traffic on port 80 and 443 and send it to NGINX’s 80 and 443 as per the previous bullet) - but how?

Add a DNS A record.