If you are not a tax resident in Estonia, your salary is not contributing to your pension. This means that you will not be able to benefit from retirement in the future. If you need it, you should look for a private pension plan.
Regarding social security, if you pay the minimum social security fee for your salary as an administrator (board member salary), you are eligible for health insurance coverage in Estonia. This would give you access to public healthcare and get medical attention in Estonia.
There is no clear jurisdiction on whether, in this case, you can opt to apply for the European health card. If interested, it’s better to ask for your specific situation to the tax authorities in Estonia.