Welcome to healthcare Magic!
Your health policy should cover whole family and these schemes are termed as Family floater
schemes and mostly cover the points you have put up but pregnancy
is not covered by most of them. This is mostly covered in the corporate health insurance which you get through your employer.
The other conditions also vary country to country and company to company.
Please read the fine print before you choose your insurer finally.
I hope the advise would be informative and useful for you.