Why use à and not aux and de not des in « à tous les coins de rue » ?

Question

I recently learnt the expression

à tous les coins de rue

When using SRS to learn this phrase, my mind instinctively puts it as aux tous les coins de rue as there is plural that follows.

I am assuming that because the preposition is followed by tous which is not a noun, we use à here. Is that right? Is this the general rule?

In addition, my mind is also having a hard time understanding why it is de rue. I am assuming it is because you should treat coin de rue as a singular unit and the plural is simply coins de rue as it is a compound noun.

Answer 1

Aux replaces à les. Here we have à tous les so we cannot use aux.
Without the tous we would indeed say aux coins de rue.

For your second question, de rue is a noun complement and whether or not it takes the plural mark depends on the meaning on the sentence. Here, coin de rue is indeed to be seen as a unit (one may argue that there are intersections but in this sentence, one corner belongs to one street) and rue stays singular.
More information and examples can be found here:
http://bdl.oqlf.gouv.qc.ca/bdl/gabarit_bdl.asp?t1=1&id=2914