A thin Easter egg shaped container in two parts, designed to click together.

No

Yes

0.15 for a smoother finish but any will do.

None

Two part egg is designed to click together, tightness of fit depends on all sorts of things like printer accuracy, filament expansion etc. Experiment with support settings based on how well your printer deals with overheads and bridges etc.
Current size is around 110mm tall with 2mm thick walls. Can easily be scaled in your favourite slicer.