Claudiu, this confusion is being caused by a misunderstanding of how MusicBee works:
When you 'play a playlist' MusicBee does not play the playlist directly but rather adds all the tracks that are in that playlist, at that moment, to the 'Playing Tracks List' (or 'Now Playing Queue') - it is this list that details what is playing, not the original playlist. At this point you can modify/edit your playlist and it will make no difference to what is played.
My advice for you to help you understand is to add the 'Playing Tracks' element to your right sidebar:

And you should then see the Playing Tracks panel like this:

It is this list that details what is being played and this list that you should modify if you want to change what is being played.
(Can a mod move this topic back to Questions)