I want to record a screencast under Linux in such way that the sound of my microphone is recorded on a separate channel than the sound of my speakers. Is there any tool which can do such screencast?
OBS-Studio - Open Broadcaster Software##
In OBS you can record pretty much any part of your screen or audio. You can choose options like window, screen etc for video and mic, speakers etc for audio.
By default these all go into the same channel but under Settings>Output you can choose advanced output mode which also allows for multiple audio channels. So you could choose 2 and set the channels accordingly.
right-click in Audio Mixer and choose 'Advanced Audio Properties'