I'd be temped to paint it white and either put a black cast iron insert in or line out the opening with brick (love the herringbone example shown below) and put a wood burner in. http://www.chesneys.co.uk/products/accessories/interior-panels/ches-brickherin

I personally would not as it might 'peel', it might not, but better safe than sorry. Let the paint thoroughly dry and if it's the same base ie Acrylic, which is most likely these days, then sand and re-paint. If you do not wish to sand, or they are different bases, then wait for the paint to thoroughly dry and then use Zinsser 1-2-3 primer or even Zinsser Peel Stop to go over the gloss and then paint with the Matt.

I’m no expert but if you want a nice clean finish it’s best to get a plasterer to skim the walls. You could try some filler like Polyfiller in the dips, let it dry hard then gently sand smooth.

Lovely garden. I had a little garden a while back that had white painted walls and lightish grey painted fence with natural decking. The grey made the fence recess and the garden feel bigger and the white reflected light and made it feel bigger too. The planting looked amazing against both because the greens really pop against the homogenised background. So I think you should paint it too, but personally I'd find a complementary grey. Cream and grey are great together.