Are skin discoloration and dark spots on face late in pregnancy normal?

Melasma. Increased pigmentation on the face during pregnancy or other hormonal changes is called melasma. It is not recommended to treat melasma during pregnancy or while breast feeding - however, thereafter, skin lighteners (including hydroquinone or other herbal products), chemical peels, and ipl laser treatments may help. Melasma can be challenging to correct, but will often lighten at least bit.
Yes. These patches are associated with the changes in hormone levels in pregnancy. They were commonly seen with the higher-dose birth control pills years ago, but that is quite rare now. These patches may well resolve after you have your baby. It is unwise to attempt to do anything to try to remove them, although light cosmetic coverage is probably ok.
Yes. Dark spots on the face in pregnancy is due to the hormonal changes you are experiencing. Often times they improve post partum but you can treat them with lasers, hydroquinone and Retin-A only after you have the baby. Neocutis has a cream called melaplex for pigment that can be used in pregnancy and using vitamin c which is weak depigmenting agent can help.