1) is incorrect. In your calculator type 20C9,20C10, 20C11. There is only one greatest coefficient.
2) Expand using binomial, you should get 9 terms, Sub x = 1/3. and you get teh result. It's a lot of calculator work...
3) Expand using binomials for each part. for example: (1+x)^n = 1 + nC1x +...