I have seen something a bit similar. Friends have a sink on the "peninsula" but it has about an 8 inch upstand behind it and then a wide shelf on the upstand that you can put things on/pass things over/sit behind on stools. It faces into the dining end of the room and the garden doors so it's really sociable.
I would rehash it a bit so the "working" end of the kitchen is well zoned off from the dining end. For instance, from the left of the middle picture:
Fridge, worktop with dishwasher under, turn corner to sink roughly where you have it and small cabinet on end. The corner could be a cabinet accessed from the other side.
(To get worktop over dishwasher, make dishwasher smaller and then use "extra worktop" or use one of the integrated ones).
On the right, cooker with good bit of worktop each side for prep & serve space, far end rounded/narrowed so there is room to walk past the sink. Beyond the sink on LHS, tall shallow floor-to ceiling cupboards for storage/larder/display etc.
You can wall mount a small flat screen TV on a discreet bracket that can either be flat against the wall or swing out, DH fits these all the time.