Who is responsible for putting stuff away, cleaning up the labs, etc.?
You are! It is your responsibility to clean up after yourself, make sure that all your samples are clearly and properly labeled (which means chemical names should be IN WORDS not chemical formulae, plus a date and some contact information), label any chemicals you are working with (the label template for this is downloadable from the Dept. web page too), make sure the chemicals are properly stored and generally clean up after yourself. Unlabeled, undated and improperly stored chemicals are at high risk of being trashed AND they are a safety violation!