The best offer is Zen card that you can buy from most kiosks. There is a start-package that costs 2.95 and includes 3 euros worth of call-time. At the moment there is a campaign where buying 1 start-package gives you two additional sim-cards that are not charged, which you can then give to other members of your group. If you charge it with at least 10eur (you buy a charging card worth 10 eur), you can call and text other Zen users for free. If you load 15 eur you can also surf the internet for free (providing you have that kind of a phone). More info from http://www.zen.ee, use google translator.

Additionally to finding flats from all of the other real estate pages (use google translate or ask teachers if there is no english option), there is also a site www.soov.ee.
This is the Estonian Craig’s List where additionally to finding a flat you can buy/sell furniture, bicycles, electronics ect.
Regarding the commission for finding a flat, its usually 1 months rent that goes to the real estate company. It is possible to find some commission free flats/rooms straight from the owner through Soov page or EKA list, but in the majority of cases you are also required to pay the commission fee.
Always try to understand your rent contact requirements, if there is no english version, let someone local check it.
Please note that communals are always extra to rent and they depend a lot on the type of the building and central heating choices. Always ask of fix beforehand the monthly average for communals with the owner or the real estate company.
Finding a place for only 10 weeks is possible, but it is good to write to the real-estate agent/company directly, as they might know some places for short term rent, that are not listed. Old town is most expensive area, for cheaper options look for places in Kesklinn (city center) area, that are still in walking distance.

Since it seems impossible for many to subscribe to the EKA Foorum (go have a try here) there is a mirror on google groups here. Google translate will help for the most part.