PS - I'll try the salt suggestion for the burnt saucepan, but cooking salt is completely unknown here in Germany, so I'd have to use table salt.
I love Allule's idea for the shower - I thought I was ingenious the way I did it, but that sounds better. After showering, I spray it with spray-and-rinse-off shower cleaner, then remain in the shower to dry and moisturise, then with the shower head in my hand (so I don't get wet again!) I spray down the sides and use two cloths to quickly rub dry the taps and other bits prone to staining. We have very hard water.
For the extractor hood that no one seems to have found an answer to yet: What is it made of? Mind is a matte stainless steel and so I can't use any abrasive and wouldn't dare use any chemicals. The only alternative is those micro-rubbers. I don't know if you can get them in the UK. They're brilliant for everything. They're little rectangles of a white, foamy stuff, squeezy but not soft. You just damp them with hot water and rub away gently. It will take ages, but afterwards, just do it more regularly and it won't be so much bother. For the big lumps of grease (I know, I have them, too - heaven knows how they get there) use one of those razor-blade-like contraptions that you get for scraping spots off the ceramic hob which doesn't scratch.
My uncle used to swear by paraffin which he rubbed on his head to prevent baldness - he certainly had a good bushy head of hair.