Do I need to give my baby a helmet if he has a flat head?

No. Depending on the type of head deformity, such as in the case of craniosynostosis or premature closure of the plates forming the newborn skull, the treatment is surgery and is emergent. Your doctor can help you know if your child has this condition.
Child health. The helmet use is based on the age of the child at time of detection. In the younger child under 6 months of age the first step is to reposition the child off the affected side and if it does not improved by 7/8 months one then considers the option of moving to the helmet.
No. Not necessarily. It depends how flat the head is. There are specialists that will measure your babies head and tell you if it is flat enough to need a helmet.
No. It depends. If the condition is mild, simple repositioning, increasing tummy time, and occasionally neck exercises are all that is needed to correct the problem (especially if it is treated very early on while the skull is still remolding). If it is a very severe problem, you may consult a specialist to determine if a helmet is medically appropriate or necessary. Best to consult your doctor.
No. Not generally. Usually repositioning does wonders, making things of interest be on the other side of the room. Of course, make sure there isn't abnormal neck tightness, and that the flatness isn't too far gone. A pediatrician can tell if a helmet is necessary, but most don't need that. Once they sit up for awhile, starting at 4-6 months, the head returns to a normal shape.
No. If a baby has a flat spot on the back of the head (from sleeping always in the same head position), the baby's head will look asymmetric. This is a cosmetic problem, because the baby's brain works just fine. If the parents want to round-out the head, they can purchase a helmet program (a custom helmet is made and must be adjusted many times) to improve the head shape and appearance.