Is it permissible for a woman to go out wearing bright colors?

Bright colors are part of a woman`s adornment, and it is impermissible for her to show it to people other than her husband, or one of her Mahrams(Unmarriageable kin).

Is it permissible for a woman to pluck her eyebrows, or to shave them and have a tattoo in their place?

It is forbidden for a woman to pluck her eyebrows, or to shave them and have a tattoo in their place since this is called (Nums), and the Prophet(PBUH) has cursed those who do it.

I see horrible dreams although I perform the prescribed prayers, what do you make of that?

All perfect praise be to Allah the Lord of the Worlds. May His peace and blessings be upon our Prophet Mohammad and upon all his family and companions.

Be mindful of Allah while awake and he will safeguard you from whatever evil you see while asleep. We advise you to make the pre-sleep supplications. And Allah The Almighty Knows Best.

A woman used contraceptive pills, and her menses exceeded(15) days, is it permissible for her to fast?

The maximum of menstrual blood is(15) days, but if it exceeded that due to a medication, or the like, then it is Istihadah(bleeding outside the monthly period), and in this case she should perform Ghusl(ritual bath), pray, and fast. Moreover, she is obliged to make up for the missed fasting days which exceeded her regular menses.