Just to repeat what a couple of others have said. The cabinet is in great condition and a good colour. perhaps change the knobs for a very simple small aged brass or even a dark bronze button type. Change the lamp as it is too big for the unit, the shade is pressing against the wall, (it could work well on a side table by a sofa perhaps). Exchange it for a lamp with some brass incorporated into it (very popular and in most decor stores now) and it could look lovely. the difference between painting or leaving the unit, depends on the final look you are going for. If you want a more classic feel. Don't Paint, go with the above suggestion. If you want more quirky as some of your accessories suggest, Then Paint and adorn with crazy abandon! Happy days!

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.