Assuming that an IP address is only assigned to you and not to other users (via a NAT that you have no control over), it's easy to occasionally ping your DNS server with your IPv4 address and assign a hostname to it.

If your DNS provider has an API, it's probably the first example in the API documentation. If not, there's DuckDNS and similar.

This is true, though there are still often port limitations. For example, with residential connections here, port 25, 80, and 443 are filtered incoming, so you can't run a web server or SMTP server on a normal port. Also servers technically violate the AUP. Business connections have no such restrictions.