Not sure where you are located so I don't have a clue what your weather is like, especially your winters. That would influence how I would set it up.
1. Where to mount the automatic feeder and waterer? (Inside or out).
In a 4x4 coop with four hens you don't have a lot of room to set up food and water where they can't poop in it from the roosts. Your coop is likely height-challenged too which can make layout a bit more challenging, maybe not enough room to protect stuff under a droppings board.
As far as whether it is best to feed and/or water inside or out, some people feed and/or water inside, some outside, some both, and some split the feed and water. There is not any one way that works best for all of us. It's your unique set-up and conditions of coop and run, weather, flock make-up, and so many other variables that could make one better for you. With your small coop the run might be better if you can keep the feed dry and you will have the weather or conditions they can get to it when they are awake. If you leave them locked inside the coop section only for long periods of time you might be better with one or both in the coop.
2. Should they have constant access to the feed or only when I allow?
&
3. How much feed should 4 teenage or adult hens be feed on a daily bases?
How much is going to depend on the size of the chickens (bantam or full-sized), age , whether they are laying, molting, or neither, how cold it is so how much energy do they need to stay warm, how much is wasted, and other variables. I free feed, which means feed is always available when they are awake, and let them decide how much they need.
Also would only 2 nest boxes work for 4 hens? I heard they like to share.
A general rule of thumb is that if you go with the minimum recommended size (12" x 12") nest box you go with 1 nest for every four hens. But for the same reasons given above I agree two should be the minimum. For only four hens any more is a waste.
1. Where to mount the automatic feeder and waterer? (Inside or out).
In a 4x4 coop with four hens you don't have a lot of room to set up food and water where they can't poop in it from the roosts. Your coop is likely height-challenged too which can make layout a bit more challenging, maybe not enough room to protect stuff under a droppings board.
As far as whether it is best to feed and/or water inside or out, some people feed and/or water inside, some outside, some both, and some split the feed and water. There is not any one way that works best for all of us. It's your unique set-up and conditions of coop and run, weather, flock make-up, and so many other variables that could make one better for you. With your small coop the run might be better if you can keep the feed dry and you will have the weather or conditions they can get to it when they are awake. If you leave them locked inside the coop section only for long periods of time you might be better with one or both in the coop.
2. Should they have constant access to the feed or only when I allow?
&
3. How much feed should 4 teenage or adult hens be feed on a daily bases?
How much is going to depend on the size of the chickens (bantam or full-sized), age , whether they are laying, molting, or neither, how cold it is so how much energy do they need to stay warm, how much is wasted, and other variables. I free feed, which means feed is always available when they are awake, and let them decide how much they need.
Also would only 2 nest boxes work for 4 hens? I heard they like to share.
A general rule of thumb is that if you go with the minimum recommended size (12" x 12") nest box you go with 1 nest for every four hens. But for the same reasons given above I agree two should be the minimum. For only four hens any more is a waste.