Hosting the site cost nothing. Using $7/mo Heroku server for API with HTTPS and custom domain. Firebase can quickly start to cost money. Domain around $32/year. So it definitely does cost money to run, but not much at all.
If you want to reduce your costs, you can have HTTPS with a custom domain on a free Heroku app by using Cloudflare. Why are you using Firebase to serve quotes? I imagine the dataset could number just a couple thousand quotes max, which is fine to serve from memory after loading from a file at startup.
Or if you're using Firebase as a convenient interface for adding new quotes, the app could update its internal cache of quotes once a day, without having to pay Firebase for each API call.
Yeah, I realized that after it started getting a lot of traffic. The problem is I kinda just made this for fun and have no idea what I am doing. Do you want to contribute? https://github.com/ajzbc/kanye.rest