Yes you can!
However, what you may want to look out for is:

1. The capacity of the droplet based of the anticipated collective load of the sites)
2. For easy site management you may want to deploy a Control Panel like Vesta Control Panel for faster easier management of all sites(i.e. if you’re not very familiar with Linux or nginx or apache. Instructions here: https://www.digitalocean.com/community/tutorials/how-to-install-vesta-control-panel-on-ubuntu-12-04-lts

In addition to the above answers, you could also use the free Cloudflare service and nginx’s fastcgi cache. The combined power of those two things will mean that 99% of requests won’t even touch the backend or database etc. I followed this guide https://rtcamp.com/wordpress-nginx/tutorials/single-site/fastcgi-cache-with-purging/ but I see there’s also a tutorial here now: https://www.digitalocean.com/community/tutorials/how-to-setup-fastcgi-caching-with-nginx-on-your-vps

I managed to hammer the hell out of a small droplet and serve several thousand requests per minute without the load monitor even batting an eyelid, because, as I said, Cloudflare served most of the requests before they even hit the server, and the fastcgi cache served 99% of the rest.

As an added bonus over something like W3TC kind of plugins, with the fastcgi_cache methods, your site will stay up even if your back end/php/mysql goes down! Neat, huh?
(Obviously only for static content, not posting comments etc!)

Yes you can, if you are using apache for the webserver you can add an virtualhost for each domain. Then point your nameservers for each domain to the listing IP of your server.