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Yes, for the first couple of days of a heatwave before the building is saturated. From that point on, it will work harder to retain the heat, meaning all things equal a well insulated property will be hotter, and remain hotter for longer, than a less well insulated property (as per design).
Of course, a property designed to be both well insulated for winters and able to cope with prolonged periods of 30 degree summer heat (with 40 deg. peaks!) should allow you to have the cake and eat it, the trouble is this isn't what we've been shooting for in the UK - the focus has been reducing heat loss, and to @hoefla 's point, regs covering overheating have only just gone in.
Yes.
EDIT: I should probably specify this a bit better. A black painted wall with insulation in it will keep out heat better than a black painted wall without insulation. But then again, you'll probably have windows in that wall, and most of the heat inside will probably be generated by the light that came through those windows, which the insulation then traps.... so yeah. Depends on your ability to let out trapped heat in summer I guess.