Building codes, or rules, have been created to promote safe buildings. There are several organizations that regulate codes, most noteably the International Residential Code or IRC as its called. Different parts of the country use different parts of these codes. This article explains some of the codes that deal with minimum sizes of spaces. Check with your local building department to verify codes specific to your project before spending time and money building.
Bedrooms and living rooms are considered habitable rooms and must have ceiling heights no lower than 7'-0".. Habitable rooms must also have a minimum of 70 sq. ft. of floor space. Bathrooms, closets, hallways etc are considered non habitable and can have ceilings as low as 6'-8". Beams may be a little lower, again, check with your local building dept.
Hallways: Minimum hallway framed widths = 3'-2". by the time sheetrock is installed and door trims the width will be 3'-0"