Moving to subdomain

Yes, it is possible, The amount of work depends upon how much active content you have. This migration may include some downtime as well.
I don’t know exactly about your setup but this guide can be a good reference for what you want:

You can do that, but it requires additional set of configuration to your droplet.
Here is a Guide for that:

That can be done but I’d recommend a LEMP stack instead (it makes things much easier)