I'm going to answer in sections.
- MusicBee starts this playlist at a certain time
To the best of my knowledge, this can't be done. You might possibly be able to use a script from within Windows, but that's way out of the discussion of this forum.
- A smart playlist (containing similar songs) with a certain duration, based on a random genre is generated daily
- Played tracks are marked so that for the next playlist not played ones are prioritized
These two on the other hand are more or less possible. Thinking about your requirements, what you probably want is Auto-DJ. If you've never used it before, it's on the left hand side in the playlists node.
When you've got the configuration screen open in front of you, you want to click on "Apply filter" and choose something like "Last played is not in the last 3 days", then have the source as Library. selection mode as random, and under restrictions, tick "Only include tracks from artists rated by last.fm as more than % similar", choosing whatever percentage you want. You could also consider ticking "Stream tracks from Xbox Music".
This will work best if your files are reasonably well tagged (at least having the correct artist and track name for example). Auto-DJ will just keep playing tracks until you stop it. To get it to stop after a certain amount of time, once you've started Auto-DJ off, go to File>Activate Auto-Shutdown. Choose "Stop Playback" @ "Elapsed Minutes" and choose the time you want.
Layouts of things have changed slightly in very recent versions of MB, so before you do all this, make sure you're updated to the
lastest patch.
Bold words in my posts are links unless expressly stated otherwise.