Because of the heat, you should not use dark colours on walls or roof. regarding painting of brick. Brick is an almost no maintenance cladding. When you paint it you've set yourself up for a big chore every 7 (on the west) to 10 years. Secondly, if you still want to paint it, you need to use special brick paint, or natural limewash. Bricks and mortar need to breathe. If they can't, you can have structural problems down the track. theres lots of information about limewash on the Internet.

Terracotta roof tiles. Then you could either go with steel greys and blues, varying shades and tones of terracotta or a combination of both. Have included some Dulux colours showing how versatile terracotta can be to perhaps give you some inspiration...

I'd pick a white quartz pebble but some of them have a rust coloured vein through them and I think that would be a nice match for your roof

Definitely look at restoring tiles. If still wanting to paint after that, then a colour like Dulux Western Myall, which is lighter than monument. Therefore better for solar passive principles. Woodland grey, does have a green undertone. You mentioned shade, there appears to be no shade over the house from your photos, so a lighter roof colour maybe better.