Minecraft does not have an API currently. If you are making mods you are decompiling the original Minecraft java source code, modifying it, and releasing a modified version of their original works.
> Installing mods is done by copying compiled .class files into the client .jar
This is no longer true, except for Forge. What you're talking about is the old-style mod system, which has been obsolete for some number of years; nowadays they're dynamically linked from iterating over the mods/ folder.
