With audacity you can import audio of the regular variety: Audio, MIDI, Labels and Raw Data. You can directly import MP3 files into the project, and mixing different song together in audacity.
Let me give you example.
First my main song "smurfesangen", and then you can import for mixing, one another song, just choose in the meny > > file > > Import Audio, then the newly imported audio will come under your first audio, the possibility to mixing here is huge.
To split the audio so you can move part of it you have to first with the selection tool, choose where you want to cut it. And then with "ctrl + I" split it. And then with time shift tool you can move the segment.
With the Zooming tool you can zoom into the audio segment and then manipulate the audio with the drawing tool.
With the envelope tool you can manipulate the volume by increasing or decreasing the volume wherever you are on the segment.
Time Shifting Tool
with this you can move your audio segments around.