Can I still grow in height at the age of 20 if I start doing stretching exercises? I am 5'6 at the moment

Unlikely. Growth does not depend on stretching, but depends on the growth plates at the ends of the long bones. If the growth plates are fused, no appreciable further growth will occur. If the growth plates have not fused, further growth is possible. Growth plates usually fuse (depending on the bone) at age 15-18.
No. Any transient gain in length by stretching,hanging upside down, etc. disappears after gravity again exerts its full effect on your body. A common myth but it is a myth.You quit growing taller when your growth plates fuse, at 16-17 in males,15-16 in females. A balanced diet/rest/exercise support normal growth.If you have not grown in the past year you are done, have a good life.
Maybe not. Boys usually have their main growth spurt in the mid-teens. Some may have a small second growth spurt after 18, but it depends on your family history. Most of the time your height velocity (how quickly you increase your height) is genetically determined. Eat healthy foods and exercise regularly, but you really can't change your height.
Probably not. Most people reach their full height by age 20, and stretching would probably not do anything to increase it anyway. That said, stretching does have it's benefits in increasing flexibility and balance, so it's not a bad idea to do it anyway.