What Linux applications can I use to make sound effects for games? For instance, what application could I used if I wanted to make the sound of a gunshot? I'm not sure if Audacity would be the right tool for this, since I don't have any recordings to work with, and don't have a microphone. I need a program that allows you to create effects from scratch.

You can't create those effects "from scratch."

You can create noise and regular patterns and pitches. If you are an audio programming expert you might even come up with sounds like the THX "Deep Note" audio logo.

There are many free and royalty-free audio libraries out there; read the FAQs for a few of them, Google will reveal many others.