You ask a most complex and far reaching set of questions which only a complete reading of Presbyterian history can fully answer. Here is a short version with many important issues and events left out, etc. (Gathered from several sources).

Knox traveled to Geneva three times to study under Calvin who had a high regard for the young Scotsman. Knox called Geneva "the most perfect school of Christ since the days of the apostles." I believe on his second visit to Geneva he was invited to become minister of the refugee English congregation. The church in which he preached there (called the Eglise de Notre Dame la Neuve) had been granted, at Calvin's solicitation, for the use of the English and Italian congregations by the municipal authorities. Knox's life in Geneva was busy. In addition to preaching and clerical work he was constantly engaged in literary work. His publications at Geneva included his First Blast Against the Monstrous Rule of Women; and his long and elaborate treatise on predestination published 1560 was composed in Geneva. The influence of Calvinism spread throughout the entire Western world and IMHO realizing possibly its purest forms through the work of John Knox in Scotland and through the clergymen and laymen of the civil war period in England and the Puritan moralists in New England.

The original Scots Reformed and the Continental Reformed were basically one in theology. English visited and studied and taught in the Dutch and other Reformed centers, and many Continentals did the same in England and Scotland. The Scholastic style and Theology was shared by both British and Continental theologians.

One of the leading Puritans was William Ames. Ames not only picked and diffused Covenantalism and the scholastic method, but he also had a strong devotional bent. Ames had also studied under Perkins, but later studied in Holland, and was at Dort. So in this period there was great cross-pollination, which even extended into the New World.

Great similarity can be seen by comparing Owen with Turretin on soteriology. Owen's treatise on Biblical theology, however reflects a Covenantal Theology that was reflected by others on the Continent. Francis Roberts, an English Presbyterian, wrote a massive work on Federal theology which is very scholastic and very similar in style to Witsius, who wrote on Federal theology much later.

Later American Presbyterian formed its own definitive character, especially under the influences of figures like C. Hodge, Dabney, and Shedd. But theologically, the American Presbyterians were one with the Continental Scholastics of the 17th century. For example, the later 17th century scholastic Turretin's Institutes formed the backbone of Hodge's theology, not only Hodge, but also Dabney and Shedd. When comparing Hodge and Turretin: the basic organizing structures in the two systematics are identical. The major differences are new issues and a new style of writing; which moved away from the scholastic method. With Hodge we have the new 19th century textbook method in Systematics. This style is replicated in AA Hodge, Shedd, Boyce, and even Dabney. Dabney was a very independent thinker and quite easily comparable to Hodge in calibre. In Scotland, Turretin also was the theological backbone of leading figures like William Cunningham.

Confessionally, the differences are that the Anglo-American Reformed (i.e. Presbyterian) made the Westminster Confession of Faith (CF) the prime subordinate standard, whereas the Dutch had the Heidelberg Catechism, the Belgic Confession and the Canons of Dort (these confessional statements were all written earlier than the WCF). The WCF theology is mirrored in later 17th century and early 18th century Continental Scholastics, like Turretin, a' Rakel, etc.

The areas of difference between Anglo-American Reformed and the Continental Reformed were mostly in matters of ecclesiology. One difference is life term eldership (Anglo-American) versus limited term elders (Dutch Reformed). This has been an ongoing difference for centuries. The Anglo-Americans tended to Post-Mil, and so did the Dutch, while those under the influence of Turretin, etc., were A-Mil. This arose mostly in the later 17th century, and into the 18th and 19th. In the 20th, there seemed to be a reversal and A-Mil gained ground.

The Dutch tended to presumptive regeneration. The English in the 17th century tended to presumptive non-regeneration. However, in the 19th century, under the influence of Hodge and Warfield, in the later 19th and early 20th centuries, presumptive regeneration came to the fore in American Presbyterianism. The Dabney-Thornwell line, which reflected the 17th century British view on this was pushed out of the foreground on this issue. Now we are back to the 17th century beliefs again, but some out cries of the Dutch presumptive regeneration still linger.

The American Reformed were more susceptible to the inroads of Fundamentalism from the 1920s onward, and often became narrow, while the Dutch were not so narrow in their outlook. Also related to this was the Anglo-American Reformed commitment to an empirical Thomist apologetic - which was also the dominant mode in all the 16th and 17th centuries Scholastics (with the only highly debated exception possibly being Calvin himself). In Holland, however, Empiricism was never popular (after Decartes and Kant that is), and so under the influence of Abraham Kuyper, a non-empirical, non-Thomist approach to apologetics was developed, which has come down to us as Presuppositionalism. Those of the Hodgian-Warfield tradition tend to be Thomists, whereas those of the Kuyper-Bavinck position tend to be Presuppositional. Berkhof reflects the Kuyper-Bavinck tradition (Berkhof is the child of the Scholastics but as mediated thru Kuyper and Bavinck).

A 1999 survey found 746 Reformed denominations worldwide. Contrary to Lutheran, Anglican or Methodist churches with episcopal structures, Reformed churches have mainly three forms of church government: (1) Presbyterian (2) Synodal—Swiss Reformed Churches, and (3) Congregational—Congregationalist Churches. Another family of the Reformed churches, called Reformed Baptist churches, adhere to modified Reformed confessions, and have Baptist views of the sacraments and of church government. This in an of itself accounts for some of the strains between the different forms of Reformed churches.

Some books for consideration:

European Reformation
Author: Euan Cameron

Reformers & the Theology of the Reformation
Author: William Cunningham

Reformation Sketches: Insights into Luther, Calvin, and the Confessions
Author: W. Robert Godfrey

Binding of God: Calvin's Role in the Development of Covenant Theology
Author: Peter A. Lillback

Reformation of the Church
Author: Ian H. Murray

Dawn of the Reformation: Essays in Late Medieval and Early Reformation Thought
Author: Heiko Augustinus Oberman

Five Women of the English Reformation
Author: Paul F. M. Zahl

The Marrow of Theology
Author: William Ames

Puritan Papers—4 vols
Author: J. I. Packer

James Ussher: And the Irish Puritans
Author: Crawford Gribben

Reckoning with the Past
Author: D.G. Hart

Defending the Faith: J. Gresham Machen and the Crisis of Conservative Protestant
Author: D.G. Hart

Abraham Kuyper: A Centennial Reader
Author: Abraham Kuyper

Reformation and Scholasticism: An Ecumenical Enterprise
Author: Willem J. van Asselt

A Religious History of the American People
Author: Sydney E. Ahlstrom

American Church Experience: A Concise History
Author: Thomas A. Askew

Free Church, a Holy Nation: Abraham Kuyper's American Public Theology
Author: John Bolt

Constitutional History of the Presbyterian Church
Author: Charles Hodge

Biographical Dictionary of Evangelicals
Author: Timothy T. Larsen

Old Religion in a New World: The History of North American Christianity
Author: Mark A. Noll

Reformed and Always Reforming,