Thanks for using Syncfusion products.
Query 1: does pie chart (or doughnut chart) allow VerticalLineAnnotation and HorizontalLineAnnotation to be added.
We have analyzed your requirements and we can able to add annotation to the pie/ doughnut series by setting CoordinateUnit as pixel. It having boundaries only if we set the coordinate pixel as axis. We have prepared a sample based on your requirements. Please find the sample in the attachment.
Query 2: the axes are not being reinitialized/reset
We are not able to reproduce the reported issue. Please find the sample in the attachment for your reference.
Please let us know if you have any queries.