When a woman is not wearing a bra, is it normal for her breasts to do whatever they want?

Well Im a guy but yes breasts come in all different shapes and sizes and when unleashed from the bra take on there natural shape whether it be tear drop rounded or cone shaped.
I think hair around the nipple is more common than you actually think for and i would say it doesn't bother me :-)

Actually, your breasts are much healthier without a bra.  The bra changes natural breast shape, and this requires pressure, which interferes with proper breast circulation.  If you have red marks or indentations in your skin when you take off your bra, then it is too tight and may be causing fluid build-up in your breasts.  This is also the cause of breast pain when women have their menstrual period.  Bras also cause the breasts to droop and get weak because they are artificially supported by the bra instead of the natural ligaments supporting the breasts. This makes the ligaments get weak from not being used.  So not wearing a bra is the healthiest thing for your breasts, and can help prevent breast pain, cysts, and cancer.

As for hair around your nipples, that is normal and guys may or may not care about that, depending on the guy.  Hopefully, your guy will care about you, breast hair or no hair.