Timing sounds fine. Or you can make the cake earlier and stick it in the freezer. This makes it easier to ice as is firmer and you don't get little bits of cake coming off. Obviously this only works if you don't want to eat any of it straightaway .
What sort of icing are you planning to use? If you're using the ready roll stuff then I find it best to put a thin layer of butter icing on underneath to smooth over the bumps. A very small dab of water should be all you need to stick the spots on.
I usually leave it out of the fridge overnight once it is iced - not had a frozen cake yet. If you're worried then stick you to your original plan. If you're using ready roll then you'dd be fine either way.
If you can, I'd leave the pink spots as long as you can - even with the ready rolled stuff, there's a danger the colour might bleed slightly (eg if the icing gets a bit wet for some reason) Apricot jam should be fine for sticking them on (seived/smooth)