Can I use Firebird in a closed-source application?
In short: Yes.
Long answer: Firebird is released under non-viral open source licenses (IPL and IDPL - derivatives of MPL). This means that you don't have to disclose the source code of your application to anyone. It also means that you can distibute Firebird together with your application, without paying any fees. However, if you do want to support the developement, you can join the Firebird Foundation, which is a non-profit organization dedicated to collect donations to support the Firebird development:
As a voting member you can also influence which new features are implemented first.
The only limitation of Firebird license is that you must provide any modifications you make to the Firebird code itself.