Question

How far north did islam spread in the 600's? How far east?

Answer 1

In the 600's, Islam spread far North and East Africa through trade and the spread of the Arabic language. The expansion of the Arab Empire in the years following the Prophet Muhammad's death led to the creation of caliphates, occupying a vast geographical area and conversion to Islam was boosted by missionary activities particularly those of Imams, who easily intermingled with local populace to propagate the religious teachings.

Answer 2

By 661, Islam had spread as far north as the present-day regions of Georgia, Armenia and Azerbaijan and as far east as the eastern borders of ancient Persia (modern day Iran), even into areas of modern-day Afghanistan. 
These expansions occurred under the first four caliphs of the Islamic caliphate.

Further expansion continued under the Umayyad Caliphate, from 661 to 750.  By the mid-8th century, Islam had expanded as far as Spain in the west and to the Indus River in the East.