Yes, but not with Pi-Hole. It acts as a DNS server - you link it (either on your router or on your device), and it acts as middleware between the net, a standard DNS server (cloudflare, quad9, etc), and your device.

To set up a VPN, you can use something like Pritunl or Shadowsocks. Keep in mind, if you're hosting at your own home, it's more useful for accessing stuff remotely rather than for actual privacy / piracy. And for that case, I'd recommend ZeroTier since it handles basically everything.

You can certainly do special stuff with it - Pi Picos in particular are great for building your own hardware. But they're really only meant for small sizes and power consumption. You really don't need to hunt down for one otherwise.