I screwed the cork in a little bit and it worked fine. So it shouldn't be a problem to close it. And I wouldn't put any liquid in either. The cork doesn't look quite so tight. For me, the corks are about 5 mm in the glass and hold well.
We apologise for the missing information. The test tubes have an inner diameter of 14 mm and an outer diameter of 16 mm. The test tubes become slightly narrower towards the bottom.