There is a big difference for EU and non EU residence. Mostly we have covered the transport tickets.
Yes, it's possible to bring your family with you.
No, it isn't. You can compare prices yourself: http://www.numbeo.com/cost-of-living/city_result.jsp?country=Estonia&city=Tallinn
During the job interview you will see how often you can visit your home country. Basically every weekend and there are possibilities to take so called "long weekends"