If you are building or remodeling, please check your building codes. In most places in the U.S., you can't call it a bedroom if there isn't a closet. Your building codes may specify minimal dimensions. 24 inches is the standard depth to fit most hangers. 18-20 inches wide was ok in the early 1900's. I've lived with these, and it was unpleasant. By the 1950's closets were usually 36-48 inches wide. That's small by current standards, but usable with good space planning. That's the absolute smallest I would use. 60-72 inches would be better. Down the road, if someone wants to use it as a bedroom, you can be certain that the occupant won't want to go to other parts of the house for clothing.

I would say white. White will reflect the true colors of your clothing better than gray.

Given the apparently large sizes of your bedroom, closet and bathroom, I don't think that "losing" space to a hallway is a problem. There is this weird idea that hallways are wasted space. They aren't. You need space to walk from one place to another. That space will exist whether a walled hallway is there or not. But with an actual hallway, you define the traffic pattern, provide a sense of separation, transition and privacy. These are all valuable and should be part of your thinking when designing a space. All that said, if you intend to hire an architect or other design professional, you'd be wise not to show them floor plans. It stifles their creativity and you'll end of getting something that you could have (and mostly did) design. Your job as a home owner is to carefully explain and prioritize your requirements for the space. These requirements should initially be about how you want to live rather than measurements and hallways.

A lot of this is going to depend upon your local codes, I think. In some places they may want it to swing in, only, and it some it may be able to swing out. In some locations, a sliding door will not count as an egress door, it would have to be a swinging door. However in many instances a door would not be necessary for the emergency egress you talk about (which I realize is not the door's primary use) if you have an appropriate egress window. I feel like a closet would have to be awfully large to have a useful exterior door in it. A closet is not typically designed for passage to someplace else on a regular basis.