Some are harder to answer than than the others.
- Wherever's cheap, and not shady. Namecheap, porkbun come to mind. I personally bought mine at OVH as it was cheap and they are an ok-ish hosting provider. You can transfer to another service once you find a more favorable deal before renewing. It's worth reading up on how the ownership, tranfer, etc works.
- Yes, as others said .xyz is usally used by spammers, so might be blocked by providers. You could use your countries 2 letter tld, depending on the restrictions they have on them. Or something generic but not plagued by spam users.
- I have several services on an i7 6700TE. Old, low clockspeeds. But 8 threads and the iGPU can handle the media transcodes I need. RAM, storage and connecrivity are more crutial IMO. Newer hardware has better efficiency and features. Look at what you need, and chose accordingly. Have enough PCIe slots + lanes for SSDs and addin cards. Have enough SATA or M.2 ports for the storage. Have enough network ports for whatever you decide to do.
- At first, probably. Don't let us stop you tho. Just don't pwn yourself by letting any traffic in and out of your home network. You'll see how much time and energy you have and need for building this and keeping it in good shape. I like to plan ahead and strive for perfection, but usually settle for good enough because of the hardware limitations and time I want to spend with others instead.
- I mean, as long as it works for you, I guess. I am not familiar with them. I run Proxmox as a hypervisor and mostly Debian containers and Alma VMs. As these are the more supported ones. If you go for containerisation with say Podman, or Docker, then the host OS will matter less.
I hope this gives you a direction at least. Others, feel free to correct me.