MANY CONGRATULATIONS!!! Yes, as has been said, with a protective mare, always keep the foal between you and her to stop her worrying about it. I would also offer your girl a treat and get a headcollar on (be patient and understanding with her at the moment) when you go to handle the foal, but I would never leave a headcollar on a mare with a foal at foot.
Your mare now needs several small wet feeds to get her digestive system working properly again or she may get a touch of colic if fed dry food only. Still give her access to plenty of hay as well of course. Does she seem ok - no rolling or too much laying down? Glad to hear the foal has been feeding, just keep an eye out for him/her to pass the first few small droppings without too much straining. If you see baby looking uncomfortable and straining to pass these first droppings, you may need to call your vet as baby may have an internal blockage that your vet will easily be able to sort out for you.
Are you still in contact with the breeder you got her from, if so, perhaps a call to her for any advice if you are concerned about anything? I think you are quite right to leave Momma and new baby alone to get to know each other and to make that special bond together, just keep a really close eye on them both to make sure they are OK. A lot of mares are very protective for the first few days/a week or so, but with understanding and careful handling, they soon relax and are happy to share their new baby with you and the family.
Again, many congratulations - please ask for any advice if you have any worries. Oh and dont worry about the spots - many horses spot out later - we waited 2 years for one of ours to finally show us its spots!!