Your questions are very broad in my opinion actually, especially concerning the relationship with other natios during a period that is generally thought to have been 80-120 years long.

The government of the Dutch Republic had for the most part of the golden age a Stadhouder as the country's leader. Which is to say: "Placeholder" as in, there is no formal supreme leader. The leadership of the country was far from democratic however and was mostly filled with the very wealthy. This class of people was called "Regenten" which is similar to the English "Regent" but now refers to a group of people. These rich people in effect had a leadership position econimically and politcally. They were often directly involved in the main catalyst behind the Golden Age, namely the shipping corporations, most noteably the VOC. They were however divided on one crucial subject: do we need a King?

Although the Portuguese invented slavetrade, the Dutch were involved in this human trafficking as well, most notably by a shipping company named the WIC. They traveled the Golden Horn, what is now South America en the british and frencg colonies in the Americas. The Dutch also found the Portuguese in the East, where they largely replaced the Portuguese strongholds by Dutch ones. Slavery was used here, but was mostly in the form of indentured servitude of the local populace.

The relationship with France and the English were fought out in many battles, most notably 4 sea wars with England. But the most notable conflict arose in 1672 which is the 'Disaster Year' as the Dutch call it. They were attacked by England, France and some German provinces.

sources: panhuyzen, derks and parthesius.