There are two ways to accomplish this: poke a hole in your home firewall and expose the camera feed to the entire open internet, then attempt to add some kind of authentication system. This is very very hard to get right, don’t do it. The other option is to tunnel your internet connection on the remote device back into your home network so it looks to your remote device like it’s still at home. That’s called a VPN.

A VPN tunnel into your home network is one way, or a VPS you control that has a similar connection into your home network is another.

You can own the server yourself. Ask a buddy if you can plug in a box in their garage, now you have an off site solution.

What kind of device? They make IP cams that push their stream to a preconfigured remote endpoint (with TLS). It would have to be a server on the public internet though, your phone probably wouldn’t work

yes its possible, but a few things generate friction, major one is ISP based filtering.

often you have to use port forwrding to connect, on ports not recognized for protocols your ISP filters out.