Pesachim 33: Juicy Fruit

Why can't that which has no value be designated as terumah? Why must terumah have a value - to the recipient? Also - when it comes to squeezing grapes, for example, is their juice considered an integral part of the fruit, or separate. And most importantly, specifically, what are the implications of that difference of perspective once it comes to tumah? Also, implications of what happens with the juice of the fruit when it comes to mulberries, etc., and the impurity of it.