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Roper's Mill was actually the May Mill, in Foundry Lane, Highfield, Wigan - about a mile from Newtown.
The proprietor Joseph Roper (c.1810 - 1896) was something of an entrepreneur, being a brass founder, farmer, and mine and brick works owner, at different times.
There were two 'Roper's Mills' mills on the May Mill site - the first burnt down as you know, the second was demolished in the 1980s.
At some stage Roper became bankrupt, but was allowed to stay on as the mill manager.
There were however, a number of cotton mills in this district, so it is possible your ancestors worked at a different one.
https://www.wiganbuildings.co.uk/building.php?id=1123

Not researching my ancestors, but genealogical research, nonetheless.
Some years ago I was researching a murder which occurred in the mid 19th century close to my present day home, with a view to writing an article about it.
When I ran out of contemporary sources, I hit on the idea of trying to find descendants of the murder victim, to see if they could help me in my research, but as is often said, I found it was far more difficult trying to 'trace forward' than back.
I was at home one evening after spending the day making a fruitless search through news archive microfilm, when an old friend and former colleague called to see me at my home.
We had worked together as police constables, and he was now on the C.I.D., at the local police station.
We were both in the mood for a good moan.
I told him about my research, and of the difficulties I was experiencing with it.
When I had finished, he told me his problems.
He had arrested a team of travelling burglars, who had been targetting garages and car workshops everywhere between Cornwall and the Lake District, stealing tools, and valuable equipment. As a result of the arrest, he had recovered hundreds of thousands of pounds worth of stolen property, and he now had to try and reunite this property with its rightful owners.
This task would oblige him to spend the next few days in the office making telephone calls around the country, and he wasn’t looking forward to it. I murmured a few appropriately sympathetic words, and shortly afterwards, he left.
The following morning, I received a telephone call.
It was my friend, speaking from his office at the police station. ‘You will not believe this . . .’ he said  . . .
He went on to tell me he had arrived in his office a few minutes earlier, to start the telephone enquiries he had told me of the night before.
The first number he had dialled was that of a garage in Mawnan Smith, near Falmouth in Cornwall.
A young woman answered the phone.
He introduced himself, told her he was on the C.I.D., and gave the location of his police station.
‘That’s odd’, she replied, ‘one of my ancestors was murdered near there, years ago’.
My friend was talking to the great great grandniece of ‘my’ murder victim.
She was fascinated to hear of my research, and asked my friend to pass on her phone number to me.
She was able to put me in touch with other descendants of the murder victim, many of whom only lived a short walk from my home, and they were able to provide me with a great deal of information.
The article has still to be written!

It would appear they are your 4th cousin once removed.
This may come in handy . . .
https://isogg.org/wiki/Cousin#/media/File:CousinshipChart.jpg

Most likely WWI.
There would appear to be all around 130 men in the photo, so possibly a company (a unit within a battalion).
Photo perhaps taken prior to embarkation for service overseas.

My widowed aunt remarried.
Her new husband was cousin to one of Paul McCartney's parents, so (at a remove) also cousin to McCartney. He didn't seem to think too highly of him!