X and Y + modifier

1) "cities and towns with interdependent economies"- In this case with... modifies towns or the entire "cities and towns" phrase

Yes, the "with" phrase modifies both

2) "London and New York, which..." - Is this a valid construction? and if yes, does it modify New Yor or the entire "..and .." phrase?

This is a valid construction, and the subordinate SHOULD modify both X and Y:

London and New York, which are large cities, are... --> "which are" indicates that we're modifying both

The GMAT will sometimes test this issue, so be careful:

Neeta and Geeta, who is in Russia, are sisters of Malik.
--> "who" modifies "Geeta"

This is NOT considered a correct construction on the GMAT.

Look at OG13 #110 for a similar issue:

"Published in Harlem, the owner and editor of the Messenger were two young journalists, Chandler Owen and A. Phillip Randolph, who would later make his reputation as a labor leader."

Here, the "his" indicates that the modifier should only refer to A. Philip Randolph, but the GMAT explanation says that this modifier "does not have a clear antecedent."