May I suggest a cap of your pavers on the wall and the a slightly darker gray that relates to the privacy fence beyond? That way horizontal surfaces and vertical surfaces show similarities and blends/blurs the separations?

As the appearance of the garden has a modernist style with the straight lines and concrete furniture how about a Mondrian influence and add a bold strip of blue? It is a pond and with the right shade it could look really relaxed and contemporary. My daughter's suggestion is a chalky lilac!

Yes.. I think you should paint, but... Why not lime wash the walls so you keep the look of timber and get the light, on trend Scandinavian aesthetic. I would go for a very light grey tint with a bright white ceiling and trim. Your fireplace and the deer would be great with this look: a rug and some white and grey cushions of differing textures would bring it all together. Coffee table candles would complete the Scandinavian look. Great room by the way!

I don't know how hot it gets in Auckland in summer (I've only ever been to NZ in winter!) but if it gets hot, then go for a pale colour. Dark roofs should be kept for cold places!