LOL!! Hayley - you have some good questions there and I'm sure others will give you lots of differing answers, but I'm not the one to ask because we do absolutely NOTHING with our foals! I strongly believe that foals belong to their Mommas and not to us and that they should be left to be babies/horses as long as possible before being subjected to what we humans think is the 'ideal' life for them.
That said we are of course out in the fields several times a day checking our mares and chatting to them, babies, being babies soon want to know more about us and will come to investigate. We crouch down to their level and allow them to sniff, nibble etc, and when they are happy we offer scratches and quiet words. Pretty soon the babies are following us everywhere, and, as time goes past, foot trimming is done with one person 'scratching' and one quietly trimming, worming also is done with scratches or allowing a human finger to be nibbled on (even when little teeth are there!) while wormer slipped quietly into the little mouth.
Never having been 'grabbed or manhandled' by humans, the babies grow up with no fears and as they get older we can push them away from us if they get a little too bolshi in their play or gently reprimand a nibble that is beginning to seem more like a bite without 'frightening' them. Once they are weaned (6 months) then we introduce headcollars - no problem, just another game! - and once happy with those being put on and taken off, we add the lead rope and go walkies - again no problem as they always follow us anyway! From then on they just learn other things on a daily basis as a natural progression - sharing a stall with a friend, having their own stall, standing quietly for gentle brushes and foot cleaning, playing with the hose ready for later bathing, the noise of clippers ready for future clipping, investigating and playing games in and out of our lorry, which is parked in their field with the ramp down, ready for loading and travelling, etc etc. There is so much they can learn/be taught from this stage onwards, no need to have pounced on them during their early 'baby' days!!
Several years ago I was watching a video/cam of a mare who had foaled several hours earlier and saw a man enter the stall, grab the foal and pull it over to a gate so that (presumably) his kiddies could fuss and stroke it. The frightened foal struggled and struggled to no avail and when released, shot back to it's worried Momma. The next day the man came back and had to chase the poor foal round the stall to get hold of it this time for more pats and strokes from the kiddies. Now I'm not saying that anyone here makes a point of roughly grabbing foals unnecessarily, but that foal's first lesson in life was to run as far away from humans as possible!!
Of course there will be reasons as to why it may be important to handle a foal in the first few days of its life - the need for a rug or medical attention etc, but I understood that your questions were aimed at a normal 'ideal' for babies? So I have given you our 'strange' way of doing things. LOL!!