Following my post about cholent, I have received inquiries about buying muslin bags in Israel.
From my experience, these sakiyot lebishul mebad are available at most health food stores. You can also order them online, for example here and here.
As to care, I have found the dishwasher to be the best way to clean the bags (just be sure to wash off whatever food has gotten stuck to them under running water before placing them in the machine).
Bon appetit!