(other applications's sounds should be played as well!)
Maybe it helps if you can tell us which applications you talk about exactly and what doesn't work - because if i play two sound files they are played and i can listen to them at the same time…
(aplay /usr/share/sounds/alsa/Front_Left.wav &); aplay /usr/share/sounds/alsa/Rear_Right.wav
I don't have a microphone, but an application reading from mircophone in shouldn't be all that different to an application reading from a file… (at the output end).
Just make sure that the output is directed to the right endpoint. Linux has multiple different (competing) soundsystems like OSS, ALSA, pulseaudio which tent to block each other.