Rear hub freewheel and casette I am having some issues with my drive trainsystem. I have changed my chain after quite a while (shame on me) with a new one, that i sized exactly on the same number of links as the old one. When pedalling however, when putting a high pressure on the pedal the chain skips.

My issue is, whether the chain is not sized properly (since I havent had this issue before) or is there a problem with worn casette cogs or the freewheel.

I get a from-factory setup of Sram casette and probably Shimano hub (not sure). The cogs are quite loose on the freewheel as you can see on the picture. I dont know if this normal, but would expect to hold firmly. 

I usually ride on tough gears, so I dont know if the end of the freehub is demaged by this as you can see on the picture, or it is the design of the freehub.



Talking about the cogs, once again I dont know if they seem to be worn, or the edges are not sharp  and look like this by design.



I would very much appreciate your advice on whether the cogs, or freehub have to be changed or it is probably just an issue with the chain length. Thanks in advance ! :)

Martin

EDIT: 
I just made a video to demonstrate how loose the cogs are. Even after tightening the lock, one can still rotate the cogs on the freewheel. Is this normal ?

My loose cogs on freehub (video on Youtube)

EDIT 2:
I also post the picture of the fron chainring. Is this worn to much, or you think this is more probably causing the chain skipping, than the rear?
Are you worried that the cogs skip on the hub? I'd consider this extremely unlikely. 

The most likely reason is that the old chain has worn down the teeth of the cassette, especially when you ride on small cogs because the same load is distributed over fewer teeth. If you happen to have the old chain around, measure the length over 10 elements (see my comment above): if 10 elements are longer than 25.9mm (from pin to pin), the old chain damaged the cogs and you need to replace the cassette. The chainring in the front is often still good because it has more teeth and wears down slower.

The image shows the interaction between a new chain and a worn-out cog. It is from technical documentation by Rohloff.

Having watched the video, I do think that the cassette is unusually loose. While it would not cause the chain to skip, it will damage the hub. I found this discussion on this site relevant: make sure to tighten the ring that holds the cassette in place. A mix of road and MTB components could be the root of that problem.