If Britain, Spain, and France were able to colonize the Carribean, establish settlements, AND send ships from their navies there, were the Portuguese and the Dutch able to do the same thing? (around the 1710's period and the specific islands, I mentioned above?)

There was certainly a Dutch presence in the Caribbean, yes. Aruba, Curacao, parts of Sint Maarten and the like were all in Dutch possession in the early eighteenth century, as well as a presence in Guiana; the Dutch were also eager and active participants in the transatlantic slave trade in this period, ferrying thousands of people from Africa to the Carribean, mostly to their own colonies - though the total numbers pale compared to those f Britain or Portugal. Nearly 35,000 people were transported to the Dutch Americas from Africa in the period of the War of the Spanish Succession, so certainly the Dutch were still active participants in Caribbean slavery and colonisation in this period. Though these figures it should be noted include Dutch Guiana - the Dutch Caribbean excluding Guiana received only about 20,000 souls in the period of the war. In any event though, that would seem to suggest commercial traffic to the Dutch colonies was continuing relatively unimpeded in this period.

I am aware that you have posed the question about the dynamics of the war in the West Indies before which I assume relates to your interests here, and I have tried since the last question on this topic to see if I can find any references for you in the wider historiography, but I have not been able to find any meaningful discussion of a Dutch presence fighting alongside the English in this period in the Caribbean. The best I can manage would be this reference from Carla Phillips' The Treasure of the San Jose: Death at Sea in the War of the Spanish Succession, in which she says:

The situation changed after with the new dynasty and the outbreak of war over the Bourbon succession in Spain. From 1701 on, English and Dutch enemy vessels, French allied vessels, and corsairs from various states all arrived in the waters bordering the Viceroyalty of Peru - the Caribbean, the Atlantic, and the Southern Sea. Their arrival created a dilemma for viceregal authorities. In the Atlantic and the Caribbean the Bourbon allies organized and squadrons from Europe to meet the challenge posed by their enemies. In the remote Southern Sea, however, the viceroy had to face the challenge largely without aid from Europe. (p93)

In general however she has very little to say about the Dutch in the book - the rest of that section goes on to describe naval entanglements with the English explicitly, which would seem to suggest only a small role for the Dutch in this period who were to my understanding, as I think I have mentioned in response to an older question you had about Port Royal, seemingly not doing particularly well mustering a naval force to fight in Europe, never-mind one capable of an extended war in the Caribbean. That would seem to correlate with other answers I think you've been given from specialists more in tune with the European historiography. It seems to be that there may have been some small Dutch naval presence in Caribbean entanglements but that it was not a significant component in the conflict there, though the Dutch were certainly active as a colonial and commercial power.

My first story starts in the final years of the Queen Anne's War (1711-13) where conflicts between Pirates, the British, Spanish and French arise, they all plan to seek control and influence in the islands of The Bahamas, Cuba, Jamaica, and Saint Domingue.

It's worth noting that Jamaica was probably not particularly threatened in this period by military aggression; the central government certainly imposes greater military control throughout the conflict and reinforces its defences with extra troops (many of who end up bringing, spreading and dying of disease and ultimately doing far more harm than good), but its main challenge was raiding on commercial lines by French vessels elsewhere in the region (even then though, the slave trade continued more or less without interruption exception for a few bad years - but massive variations from year to year are normal in the history of slave trading in the Atlantic). The island itself emerged essentially unscathed from direct military entanglement and was largely left alone during the course of the war. To my understanding, conflict from the British perspective was largely focused in the eastern Caribbean, around the Leeward Islands. Places like Nevis and St. Christopher certainly fared much, much worse.