1) How can I use a dictionary to translate payer [something] à [location] 2) definite article?

Question

Le RAFEO est un programme d'aide financière visant à vous aider à payer vos études au collège ou à l'université.

QUESTION 1)
I do not understand how to use a dictionary to translate "payer vos études au collège".

Here we have "payer [noun] à [noun]". I know (from the English brochure) that this is supposed to mean something like "pay for your studies", though I don't know if it's actually grouping "études au collège" together ("pay for your studies belonging to the college") or instead it's "payer [noun] au collège" ("pay for your studies to the college").

The wordreference page for "payer" does not have an entry for payer à, so I'm confused on how to understand "au collège".

And some of the entries are confusing to me: one entry seems to have an entry "pay something" (as in "pay rent money"), and another entry seems to have "pay [for something] [some amount]", though I don't know how to read the second definition in the dictionary:

a)

This seems to say "payer [noun]" means "to pay by handing noun (to someone)". Here, the rent (ie rent money) is being given over.

Thus, this definition is not applicable for "payer vos études", since you're not paying the school by somehow handing over your studies (ie, handing over your textbooks and notes and assignments?!).

b)

This does seem to say (by looking at the example sentences) "payer [noun1] [noun2]" means "pay for noun1, the amount of noun2", but I only understand that from the example sentences. From the definition itself, I am confused, because the French says "payer [qqn]", and the English says "pay [sth] for [sth]". There are two [sth]s in the English, but only one [qqn] for the French; how am I supposed to understand where the two [sth]s come from, by reading this entry?

Questions:
1a) Does "payer vos études au collège" mean "Pay for your [studies belonging to the college]", "Pay for your studies [(by giving money) to the college]", "pay for your studies [(while standing) in/at the college]", "pay for your [studies at the college]", or something else?

1b) How am I supposed to know if I'm suppose to group the à with the verb payer ("payer à"), or instead if I'm supposed to group the à with the "études" (so that it's "payer [noun]", where the noun is "études au collège")?

1c) How do I use a dictionary to understand "payer vos études au collège", ie "payer [noun1] à [noun2]"?

1d) How do I underestand the "payer" dictionary entry (shown above) that has one [qch] ("payer [qch]") but two [sth]s ("pay [sth] for [sth]")?

QUESTION 2)
In "payer vos études au collège", why does collège use the definite article? That is, why is it "au collège" instead of "à collège" or "à un collège"?

Answer 1

1A. It does mean "Pay for your [studies belonging to the college]","pay for your studies [(while standing) in/at the college]", "pay for your [studies at the college]" since these three seem to have a pretty identical meaning to me. You could also translate to "Pay for your [college studies]"

1B. Not much to do here but looking at the context of the sentence and identifying the correct word groups i'm afraid

1C. Again the problem you have with the sentence is that you weren't searching for the intended sentence structure, and for the other cases, here's a valid example: "Payer le loyer au propriétaire" => "Pay the rent to your landlord"

1D. I don't understand very well what you mean by that, but in most cases when there are two subjects in an english sentence it's also the case in french (see your problem above for this particular case)

2. Because here it's not the college as in national college of Paris for example, but college as an institution (like "you're a college student")