First of all I would like to say thank you for this amazing software.
So my first question is where can I find clustering algorithms in yWorks in order to have each group or cluster surrounded by a frame as can be seen in the below link of yEd HTML.
Second, is there a way to have a node divided into two, three, four, or more symmetric colors rather than one filled color?
What product exactly are you using? One of the yFiles programming libraries (if so which one), yEd Live, or the classic yEd desktop application?
yEd does not support all the clustering algorithms available in the yFiles libraries, but it does support some of them. Please see "Grouping" -> "Auto Grouping". Grouping type "Natural Clusters" is the "Edge Betweenness" algorithm from the yFiles library.
Regarding your second question, I have to admit that I do not know what "symmetric" colors are. Still, the examples given in Is it possible to add a third fill color in a node? might be of help. Additionally, it is possible to use images and SVG documents for nodes. Please see How can I use my own node symbols in yEd? for details.