Please help me understand some principles for the use of determiners. For example, why can't we say:
"the these apples" while we can say" the many trees"?
and is "All"in "all the students were on time" cosidered a determiner or an adjective?
In your first example--"the these apples"--you are using the article the (also, a determiner) right before these, a demonstrative adjective, which is also a determiner. Although both determiners can modify the noun apples, to use both is redundant. In short, you can use one, but not both, determiners because each one modifies the noun in exactly the same way. For the example "the many trees," we have the count/non-count determiner the, which modifies the noun trees--in other words, the tells us which trees--along with a quantifier adjective many. The determiner the is necessary to denote the trees to which you are referring, and the quantifier many tells the reader that you are referring to an indefinite number of trees. The sentence "The many trees in the forest were destroyed by fire" is grammatically correct, but a more idiomatic version would omit the article the--"Many trees in the forest were destroyed by fire."
In "all the students were on time," all is both a quantifier denoting the number of students and an adjective modifying the noun students. All is considered to be both a count and non-count quantifier, as in "All of the students are here." In this example, all is a count quantifier because it refers to students who can be individually and specifically counted, and all is also a non-count quantifier, as in "All swimming is forbidden unless a lifeguard is present," where swimming denotes only one action that may be carried out by any number of swimmers.