Hi Yannis, your Estonian company is a different entity from you. As such, it would require a different type of insurance to cover it from a liability with regards to your business offerings. Because the company is EU based, you would do well to look for insurance cover for the region and any other location you plan to serve. You should have some options of insurance providers on the E-portal.
Your personal insurance is better gotten in the country you reside.
With regards to tax, your company should only be paying tax to Estonia and depending on where you are from and the existence of any tax treaties with Estonia, you should not be paying personal tax form your earnings as an employee form your Estonian company.
Having said this, you have the services of tax professionals, accountants and lawyers on the e-portal available to your company. It will be best to engage their services because there is just so much to know and so many changes all the time.
Good luck and enjoy your adventure…