How many corners does a semi-circle have?

From a rigorous mathematical definition, none. It is simply a curve that is half of a circle, so has two ends, no corners. In common use, however, the term is often applied to a shape which includes the diameter which would connect those two endpoints, forming a closed shape instead of an open curve. It is even more loosely used to refer to the whole of that shape - the interior as well as the exterior curve and line - which is more accurately called a half-disc.

https://en.wikipedia.org/wiki/Semicircle

Does the figure formed by a semi-circle plus diameter have two corners? If by corner you mean what mathematicians call a vertex, then the answer is no - a vertex is formed when two lines meet, and here we have a line and a curve. There are two points of intersection.

https://en.wikipedia.org/wiki/Intersection_(geometry)