Thanks everyone for the replies.

I watched this video already and many more on the web. I wish this guy challenged himself a bit more by showing how to do gear maintenance on some old bike, not a brand new one where the gear is sparking new!

Anyhow, my problem is not with the limiting screws as it is with the middle range gears. I have managed to play a bit more with the tension cable and it seems to be working slightly better. Not perfect, but perhaps I think at some point I might just replace the cable and the housing and see if that helps. Problem #2 still stands, where the little flywheel seems to be sitting right on top of the 5th and 6th sprockets. I have marked this with the two arrows in the image below:



Any idea on how to fix this?

Thanks again!