Have I incorrectly fed chain into the rear mech hanger So I've had to change my chain because my indicator says it's worn. It did also seem to stretch quite a lot more then the new chain.

I think I may have fed it into the rear mech hanger incorrectly since it now skips every time I pedal instead of occasionally.
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On my rear mech hanger there is clearly a metal tab going across the width of the mech. Does the chain have to go underneath it or over it. 

If it's under, it seems impossible unless I take the bottom jockey wheel out. but I don't want to dismantle and make matters worse.

I can see why this can be confusing. The picture above I omitted the chain on purpose so it was clear what I was referring to

I had it routed like this



Is it correct now?

How about my front chain rings. They don't look right to me but am not a mechanic.



Chain link image.
Your chain is set up correctly in the second picture. It should go over the metal tab.

The reason your chain is skipping is probably because your cogs are worn out. If this is the case, you should replace your freewheel/cassette to avoid destroying your new chain.