To what extent is wearing the color red forbidden for men and women, and does the ruling on wearing it differ between inside and outside the home?

There is no harm for a woman in wearing red clothing, whether at home or outside, provided she does not wear it in front of non-mahram (definition) men, as it may be considered an adornment. As for a man, the correct view is that it is permissible for him to wear red clothing, unless it is dyed with safflower or saffron.