Just a quick question here. Does držet se mean "holding on to" in the physical sense (as in, say, a strap in a tram), or does it also mean "keeping" (as in, "Why are you holding on to those shoes? They're really beat up; you should throw them away!"), or both? Thanks!
It has the physical meaning - Drží se tyče v metru (a pole on the subway), drží se dveří (door) atd.
It's not used for "keeping" things such as in your example with shoes, BUT it can definitely be used for "keeping" with abstract nouns. E.g. "Drží se svých ideálů" - He/she's holding on / sticking to his/her ideals. or "Drží se svých představ." - ideas/conceptions, or "Držíme se plánu." - We're sticking to the plan / We stick to the plan.