Can I have more than one domain on the same Droplet?

There are no limits as to the amount of domains you can point at a Droplet and you can serve multiple websites from a single Droplet.

If you are using Apache to serve websites on your Droplet, you will want to set up your Apache virtual hosts to host multiple websites.

If you are using nginx to serve websites on your Droplet, you will want to set up nginx server blocks to host multiple websites.

There are a few ways to install an SSL on your Droplet, depending on where you get the certificate from.
Apps do not have static IP addresses so you cannot point an A record at an app.
Use Punycode to add a non-ASCII domain name with DigitalOcean