This is an interesting question but I'm not sure there are definitive answers.
Rose Hill was originally just the area around Rose Hill House - see the tithe map from 1836-51 - when Rose Hill House and the old cottages on Stockport Road were all that was there.
Going up Stockport Road towards Marple the next area was Norbury Smithy - around the Jolly Sailor pub (no longer there of course).
So Rose Hill has sort of grown up over time and the boundaries have blurred but looking at the early maps I would say the boundaries were loosely Cross Lane, Bowden Lane, Dark Lane (now Dale Road) and down to Throstle Grove.
Interestingly, Hawk Green isn't on the 1836-51 tithe map. Then it was called Half Green.
The name Hawk Green first appears on the 1875 OS maps, and then the boundaries looked pretty clear as there was so little development. I would say that the canal is the main hard boundary that remains and everything else has sprawled towards Church Lane, the Ridge and Windlehurst Road.
But these are just my thoughts. Have a look at the amazing resources provided by the Cheshire Tithe Maps and form your own views:
https://maps.cheshireeast.gov.uk/tithemaps/