Residents of the Old Charleston District

X have explored Y, whose shingled roofs were clustering..."shingled roofs" refers to Y?

Correct

X have explored Y, with shingled roofs clustering..."shingled roofs" refers to X?

with shingled roofs clustering is appositive modifier which can modify preceding noun or preceding noun phrase. Since preceding noun(sidewalks) does not make sense, appositive modifier modifies noun phrase
Check out more on this
https://www.beatthegmat.com/mba/2010/06/ ... -modifiers

+1 for D

whose - relative clause usage refers to immediate noun hence sidewalk,here.Hence POE.

D is correct usage.

Residents of the Old Charleston District have explored winding streets and
saw cottages nestled on the sidewalks, whose shingled roofs cluster
together like beads on a string.

A: saw cottages nestled on the sidewalks, whose shingled roofs cluster
B: saw cottages nestled on the sidewalks, whose shingled roofs were clustering
C: saw cottages nestled on the sidewalks, with shingled roofs clustering
D: seen cottages nestled on the sidewalks, with shingled roofs clustered
E: seen cottages nestled on the sidewalks, whose shingled roofs have clustered

First step: Parallelism, note that "and" is a parallelism marker where X, Y should be parallel. X element is past participle: "have explored" Y should also be in past participle:
A: saw cottages nestled on the sidewalks, whose shingled roofs cluster
B: saw cottages nestled on the sidewalks, whose shingled roofs were clustering
C: saw cottages nestled on the sidewalks, with shingled roofs clustering
D: seen cottages nestled on the sidewalks, with shingled roofs clustered
E: seen cottages nestled on the sidewalks, whose shingled roofs have clustered

Second step: Concision
D: seen cottages nestled on the sidewalks, with shingled roofs clustered
E: seen cottages nestled on the sidewalks, whose shingled roofs have clustered

more input please on the distinction between:
(i)"cottages nestled on the sidewalks, with shingled roofs..." and
(ii) "cottages nestled on the sidewalks, whose shingled roofs..."

does "with" (a preposition) modify "cottages" unambiguously?
also, does "whose" strictly modify "sidewalks" (the nearest noun) all the time?