Thats a lot of questions! I will try and answer them all.
First of all, we have 18 goats which is probably more than you are thinking of, so it will take you considerably less time to complete your routine than it would us. Normally someone goes up to the goatshed at about 7am, the milkers are milked, given concentrated food, water and hay topped up if need be. If it is summer, the goatlings are put out in the field, if not summer they are given some breakfast first. In spring/summer, kids need to be fed their morning feed of milk as well. Back down to the house, with the milk, strain it, put it into fridge to cool.
The goats then get put out in the field once they have eaten breakfast- about 9 am generally. If it is REALLY wet they don't go out at all, but generally the younger goats will get put out even if it is drizzling.
If they are out in the field, they come back in at about 6pm, they are left for a while to rest, then we milk again about 8pm. Milk, feed, water, hay is all done again.
So we milk twice a day, and we do not let the mothers rear the kids at all. We take the kids away soon after they are born, and bottle feed them. This way, we know how much milk mum is giving- and also how much the kids are getting! There are other ways, you can leave the kids with their mum for a few days, then take them away, or you can leave them until the kids are weaned, and just help yourself to some of the mum's milk.
We do now have a milking machine, but have hand milked (in the family) for over 40 years. We still do hand milk regularly to keep them used to it. It only takes 5-10minutes to milk one goat by either machine or hand. It does take longer to milk when they have newly kidded, and when you aren't used to milking them as well. They can kick more when they have recently kidded until they get more used to it.
Our goats are primarily stall fed, although they do get out. We keep them mainly for show, with milk production a big importance to that, so they get fed quite a lot of concentrated food. During winter months (November- February) they are not out at all except for walks and outings for exercise. During winter we try and divide up the feeds more through the day. Concentrated food am and pm, extra hay at 2pm, and another feed at 5pm (usually soaked beetpulp, alflafa or chopped vegetables). Dried nettles are good if you dried any during the late summer as an extra treat.
All in all, if you are aiming to have 2-3 goats, with maybe 1 milking, it should take you maybe 30-40 mins morning and evening. Ideally another 15mins or so during the day if you are around.
We deep litter our goats, so they are mucked out about 3-4 times a year, and have fresh straw given to them at regular intervals.
Hope that helps- feel free to ask more questions if anything I have said doesn't make sense.
Beth