No, ActivityPub is a push protocol. Other instances send data to your instance via HTTPS and only HTTPS. So you need at minimum a public domain and web server with TLS enabled.
Some people use Cloudflare tunnels to avoid opening ports or just get a cheap VPS to forward the traffic home without exposing the home IP.
Absolutely. However I feel like the whole thread needs extra clarification, considering the question OP posed.
Dynamic DNS isn't a magic wand in the way a Reverse Proxy over VPN is.
Yea, that is also what I thought. To bypass this, you would need something like Cloudflare Tunnels or setup a VPN on a VPS, that redirects traffic to your homeserver.
Duckdns is pretty much a service that offers free domain names.. that could point to any public IP.
(I have seen setups where local IPs are used just for HTTPS).
So its good for instances as HTTPS can be achieved without buying domain name.
I'm not sure I understand the question. They are used to encrypt traffic and prove that the entity hosting the site hasn't changed by using a digital signature. These two together make it so third parties can't read the traffic coming through. This is a requirement for modern internet. Otherwise your passwords wouldn't be a secret because literally anyone would see them.