How did cross-cultural interactions arise in isolated areas between 1000 and 1500 CE? (See below.)
Explain how demographic growth, increased agricultural production & economic expansion helped bring cross-cultural relationships into isolated area such as sub-Saharan Africa and Western Europe between 1000 to 1500 C.E.
The basic idea here is that all of the things that you mention led to an increase in trade. As trade increased, people who had once been isolated started (for better or for worse) to interact with one another.
In Europe around 1000 CE an economic boom happened. With it came higher populations and greater wealth. People started to want to trade because they could now produce excess goods that could be traded for things that they could not make themselves. This led to a gradual expansion of trade. First this trade was relatively localized, but eventually it spread to the point that Europeans were sailing down the west coast (and later all the way around the southern tip) of Africa.
Basically, then, the more you have increased agriculture and economic production, the more you have population growth and a desire to trade with others. This is what caused the cross-cultural interactions you mention.