UPDATE
It's amazing what you can do with a spanner these days. Hanger's been sorted.
Shifting is the problem at the moment. A gear was not getting in so I ajusted the H and L screws and it shifts fine now, but the chain is not properly alligned with the sprockets so it makes a sound that gives me the impression that the bike is going to fall apart...
Also when I shift the front gear down to the smallest sprocket, the part of the chain going in the Guide Pulley comes in contact with the chain leaving the Tension Pulley of the rear derailleur, I don't know if this is normal but it definitely doesn't look normal.
I think it's a matter of getting the angle of the whole rear derailleur right.
I do enjoy fixing my bike, I am aware that I don't do things properly but I hope that I will manage to get it running flawlessly in the end and that I learn from the experience. I get the tools from my next door neighbour and all information from this forum and google.
Thanks all for replying!