Real-estate purchase is relatively condition free for non-Estonians. It is worth mentioning that buying real-estate is not directly linked to obtaining a residence permit though as it is in some countries.
The main websites that list the available real-estate are www.kv.ee and www.city24.ee - both of them also operate in English. The actual real-estate purchase agreement has to be notarized and the ownership has to be transferred in the Real-estate registry (or in other words Immovables Portal: https://kinnistusraamat.rik.ee/detailparing/Login.aspx?ReturnUrl=%2fdetailparing%2f). The Portal is an effective way to check the ownership status and also other important aspects such us collaterals that are linked to the real-estate in question. Although it is a public database, the enquiries are not free.
The notary fee and the state fee related to the purchase are relatively low - mostly parties agree that the buyer pays for the related costs but that is a question of negotiation. The whole process is relatively smooth and fast. Finding an English speaking notary might not always be speedy but you can always find someone to translate.
There are a few restriction for people in regards to the type of real-estate. For example regarding the plots of land on the border areas due to national security reasons. Also agricultural land and forest land could require a permission from local authorities but buying an apartment has no real restrictions.