Can you access a server from anywhere?

Install the server software on your local PC. Use the Internet router to forward the server port on the LAN to the WAN connection. Exact steps will depend on your router model. Access your server via its IP from anywhere.

How do I connect to a server without a public IP?

A VPN is a way to tunnel a connection to one network through another network. As such, it does not need a public IP address. You have a working VPN from your ISP’s network to your local network.

Can a computer be used as a server?

Pretty much any computer can be used as a web server, provided it can connect to a network and run web server software. Since a web server can be quite simple and there are free and open source web servers available, in practice, any device can act as a web server.