Do red leaves also photosynthesis? How? Do they have same photosynthetic pigments as Green leaves?

Green leaves contain chlorophyll, which is the pigment that makes the leaf go through photosynthesis.  Red leaves do not contain chlorophyll, (they contain kerotin) so they do not photosynthesize.

Yes they can photosynthesize. Even though your leaves may show red coloring (carotenoids), they still contain chlorophyll and can undergo photosynthesis. There are lots of plant leaves that have reddish-colored leaves on the underside of the leaf. This is just a genetic inheritance from the parent plants before that contained carotenoids. Even though you may have a plant that has bright red leaves, there are still trace amounts of chlorophyll embedded into the leaves themselves. Red pigment is carotenoid, green pigment is chlorophyll.