Hi bloggie - thanks for your questions.
Regarding opening a bank account in Estonia, it's important to note that this would be a up to the bank itself, which would make the decision based on your individual situation and in line with its own company rules and KYC policy.
Regarding your question about taxes, please read our FAQs, in which we cover this topic: https://medium.com/e-residency-blog/faqs-about-estonias-digital-nomad-visa-b04f12551e30.
And as regards your final question, this is a migration issue and so should be put to the Estonian Police and Border Guard migration service. Their contact details are in the FAQs.