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You mean like this?

https://github.com/seven1m/do-install-button

A cheap $5 droplet can run 20 instances of this, probably.

I don't know about 20 instances. It uses up about 173MB of memory on my instance.

Yeah, probably not 20. See related comment thread: https://news.ycombinator.com/item?id=11013579

I believe so considering this is just a client for the most part, so long as you don't have 10,000 people trying to use it all at once.

I did in fact run this on a cheap $5 droplet, along with an apache2 server. Worked fine except it crashes about once a week, I think due to memory usage. I switched to weechat in a tmux session