In connection with a short break, now I answer your questions
I know the city of Köthen in Germany, near Magdeburg. Köthen is written in German with a Umlaut on the O. Cothen in the Netherlands is written differently and also a very small village. There is no relationship between these places.
Holland, like England was a land of seafarers and koloniesators. There are many Dutch peaple gone to South America. Brazil was a Dutch colony for a while and until recently, Suriname (Dutch Guyana) and also some Antillean islands.
Some sites also can be viewed in English:www.geneaknowhow.netwww.genlias.nl
Note the way of writing
Henry of Cooten may also van Kooten (Cooten is an old spelling)
De Rycke is an English spelling. Databases can help you find it on de Rijcke or de Rijke
Friday I go on vacation. In July I'm back and I will try to find the Rycke and Hendrik van Cooten in severel databases