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It looks like that's something they hoped to have in place for 2017, but still is not possible. From the official website FAQ at https://e-resident.gov.ee/faq/

"Visit the bank office in person and apply for a bank account. The bank will want to know how you are connected to Estonia and how you plan to use the account. You will need to bring your e-residency card along."

Registering a business should not be a problem.

In terms of opening a bank account, SEB now offers a way to do that through a video meeting: http://www.seb.ee/eng/remote-advisory, although right now if you're not yet a client, you can not use it. They promise to open it up for new clients as well, but no ETA I think.

Have you tried calling the local Estonian embassy/consulate? Not sure which country you're in..