Greetings from Syncfusion.
Query 1: Kind of confused which control is more suited "Carousel or Rotator". I do need to be full screen and with dots and ideally using custom views (xaml only).
SfRotator control is suitable for your requirement, because carousel control doesn't have any navigation stripes.
Query 2: SfRotator with button in datatemplate doesn't fire the click event.
We have tried to replicate the reported "SfRotator with button in datatemplate does not fire click event" issue at our end by created a sample based on provided code snippet. Since we are not aware of your exact application scenario, so we request you to try our sample and can you please revert us by modifying the sample based on your application along with replication procedure.
This will be helpful for us to investigate further and provide you a better solution at the earliest.
Please find the sample & video from below link
Note: We have checked with following devices, Moto E2(API 23), Moto G4(API 24), Samsung SM-G50F (API 26). Please let us device configuration for provide a better solution.
Muneesh Kumar G.