This is a pretty open ended question, but what you're asking for will be covered in any DAW (Digital Audio Workstation).
1. Realistic-sounding drums track writing;
You will most likely achieve this through a VST plugin. http://en.wikipedia.org/wiki/Virtual_Studio_Technology . People write drum plugins that will work with any DAW that supports VSTs, which is almost all of the popular ones. "Realistic sounding" is a little subjective, because no plugin will perfectly capture the real thing, but they can get close, and maybe that is good enough for you.
2. Catch MIDI keyboard input and applying synth effects to it;
Again, this will most likely be done with a VST plugin. All DAWs will allow you to record midi, and there are countless plugins that will take your MIDI instrument and turn it into whatever you want.
3. Record audio from microphone;
Any DAW will do this. How is your microphone plugged into your computer? Through the mic jack on your computer, or do have an external sound card? Either way, this is one of the most basic functions of any DAW.
4. Basic audio manipulations like equalizing, pitch, volume control etc.
Almost all DAWs have basic effects, and you can get other ones, and again they will be VST plugins.
What DAW is best for you? I'm assuming that you have Windows, because you said you're using
Audacity is free, and you can get a plugin that will allow you to use VSTs. That would probably be enough for you to get started. Other than that, there are plenty of non-free DAWs to choose from. You've probably hear of
ProTools, and there is also
Reaper, etc. They will basically all do the same thing for you though, and if you're doing this non-professionally, and you don't have a bunch of expensive gear to plug in, then I would go with the free option.
Audacity - http://audacity.sourceforge.net/