Conducting trade fair is challenging in Tallinn. You need very good marketing (that is not cheap), also venue rent and running costs are what stops most of the trade fairs from being profitable in the end of the day. I would recommend to get in touch with local communities of enthusiast of Indian / Rural / Handmade topics and explore it further. You can easily find them in Facebook.
Answering your questions: best time is from April till September. Instead of planning one long-lasting event for 7-10 days, I would recommend to conduct a tour via Estonia, staying 1 day in small towns (Tartu, Pärnu, Narva, Viljandi, Rakvere), and 2 days in Tallinn.Best places for the venue are large shopping malls, if you are looking for 100-500 sq.meters.
If you need more, then in Tallinn look for (google websites and contacts):
1) Saku Suurhall
2) Tallinna Lauluväljak
3) Eesti Näitused