I'm 27 and I'm having a hysterectomy soon due to endometriosis. Will that put into menopause will being in menopause affect my mental health.

Ovaries too. Only if they remove your ovaries too. If they are, talk to your doctor about hormone replacement therapy, it can significantly mitigate the side effects you may experience.
Depends. If your ovaries are removed you will be menopausal right then. If your ovaries are not removed, you will eventually go through menopause, usually around age 50. Keeping your ovaries does present the risk of persistent or recurrent pain due to the endometriosis.
Ovaries or not. You will only be in menopause if your surgeon is also planning on removing both of your ovaries. If your ovaries are not removed, you will then go into menopause when your ovaries stop functioning. The average age of natural menopause is 51 years old.