Yes you do need to create a droplet in order to use the domain name.

To host your websites you decide if you want one or more droplets.

SSH is not necessary to access your droplet but it is recommented.

See the link bellow on how to use ftp. https://www.digitalocean.com/community/articles/how-to-use-filezilla-to-transfer-and-manage-files-securely-on-your-vps

To create databases I suggest you use phpmyadmin as an interface of mysql database
https://www.digitalocean.com/community/articles/how-to-install-and-secure-phpmyadmin-on-ubuntu-12-04

I would add that it is pretty critical to have technical know how of how to run and manage a server via SSH to get anything up and running on a droplet environment. A droplet is essentially your own little computer up in the cloud and you need to know how to set it up :)

if you dont know how to set up the basic linux server then I think it is better to stick with shared hosting or managed vps