Can you still deliver a healthy baby if you didn't know you were pregnant for the first 4 months?

Late prenatal care. Yes. Go see an obstetrician and start getting prenatal care. Many women miss the early symptoms of pregnancy, but when they start to fell the baby they seek care and have healthy babies.
Depends. If you have a generally healthy lifestyle I would consider any risks minimal. Binge drinking every night might be another matter. Many of the benefits of early prenatal care help mom as much or more than the baby, since the baby extracts the nutrients it needs to develop from your body. The extra vitamins and nutritional balance you are advised to do help keep your system intact. Get started.