Not sure what your budget is, but how about a Pergola? It would look absolutely beautiful, doesn't cost a bomb to install and you could add some fast growing vines, be they flower or grape, or a mixture of both, whip the slabs up, lay a plastic membrane and then whack a couple of tons of peashingle down. To finish it off, I would remove the wall in front of the patio and replace it with some large planters containing box hedging, rosemary, or lavender. A little touch of the continent, right on your backdoor step and you won't even need to go through passport control!

I have Brazilian slate. I had same issue when installed. So i used brick and slab cleaner from screw fix if i recall. Will add a photo of each i used in a bit. I then sealed them using a cheap slab sealer. Perfect, nothing wrong. cost about 20 quid for botha and 5 litre cans. They are now water proof, but slippery when wet especially with flip flops. opps.. Remember, if you need to allow soak away, you may not be able to use sealer as it creates a water barrier. but if its just in the garden on level ground sloping away form house you should be fine to go. As soon as dry, they are as good to go as before, but clean remember to let completely dry and needs 24 hours of good weather to dry. Use at least 2 coats. works a treat.!!!

The pipe into the drain, what's it from? If an appliance and this is going then the drain can go. If it's a drain from a sink that is staying then the drain will need to be moved. Not a difficult job for a builder.

I agree, you need something along the front of the porch to visually minimise the height of the wall below the window.