What was the early American church like? Which denominations were prevalent among the churches of North America in the late 17th century and 18th century? 

During that time, was there significant of cooperation or communication between church groups in America and the rest of the world? 

When did the first "American denominations" emerge in earnest?
Denominations prevalent in North America in late 17th and 18th centuries:(In approximate order of arrival or apperance) [Note: there may well have been others; these are the ones that come to mind in an overview.]

Roman Catholics, principally in Canada, the far North of New England, and the colony of Maryland;

Anglicans, both the Puritan subset, in Boston, and more mainline flavors in other Southern colonies (e.g. Virginia);

Baptists (originated in Rhode Island under Roger Williams);

Lutherans, first in New Sweden / Delaware, and Pennsylvania, and to a lesser extent in other places.

Dutch Calvinists, in New Amsterdam (under the Reformed denominations) and Scots Calvinists (who eventually became the Presbyterian denominations)

Quakers, in Pennsylvania

Methodists, in Georgia, and other colonies.

Moravians and Mennonites / Amish came to Pennsylvania and North Carolina during the 18th Century.

The most significant communication and co-operation between Christians in the New World and in the Old would likely have been among the Roman Catholics, and the Anglicans.

The first "American denomination" was the Baptists, and the Congregationalists, who evolved form the Puritan Anglicans in New England.