Sometimes it is just good to know who should you contact with your questions. Here is the list of authorities that might be useful for you:
Short-term employment, residence permits, issuing documents - Estonian Police & Border Guard Board
Settling in Estonia - Migration Advice
Visa requirements, consular info - Consular Department of the Ministry of Foreign Affairs
Population registration, residence registration - Estonian Ministry of the Interior
Customs clearance, taxes, employee registration - Estonian Tax & Customs Board
Education - Estonian Ministry of Education and Research
Health insurance - Estonian Health Insurance Fund
Social benefits and pensions - Estonian Social Insurance Board
Car registration, driver’s license - Estonian Road Administration
Unemployment registration, job search - Estonian Unemployment Insurance Fund
Evaluation of foreign documents and qualifications - ENIC/NARIC