I got the answer for this question from LeapIN. I am pasting it here, in case someone has a similar problem.
- no tax residency in Estonia - no benefits at all
- Board Member Salary + Tax Residency in Estonia = Health insurance, but no pensions
- Employee Salary + Tax Residency in Estonia = Helth insurance + Pensions + Unemployment (with a ~4.6% total surcharge for last 2)
As for the benefits- if you are not resident in Estonia, then even if you pay the minimum social tax (155,1 EUR per month) in Estonia you still won’t have the health insurance. In order to get the health insurance you should become Estonian resident.
Also please note that if you become Estonian resident, then in order to receive the pension, then you should pay the employee salary which is taxed with income tax (20%), social tax (33%),unemployment insurance (company pays 0,8% and the employee pays 1,6%) and pension tax (2%). You should also join the pension fund. The board member salary is taxed with income tax and social tax and if the minimum of social tax (155,1 EUR per month) is paid, then you will receive the health insurance but no pension fund.