your board covers way too small an area of the image. with such pictures, you will have a very hard time accurately estimating the intrinsics.
OpenCV can’t handle partially occluded/invisible checkerboards. the corner detection isn’t the issue. associating found corners into a grid is the issue.
I have ideas on how to make regular checkerboards “detectable” even if they’re partially occluded/invisible, but not the free time and specific motivation.
if you need to handle partially occluded boards, you’ll need to use “charuco”, which is a different board type.