I would argue that Salford Quays is close enough that a station at Old Trafford would see commuter traffic from there during the week. Especially from passengers from Warrington (and beyond) who wouldn't need to travel to Deansgate and then walk / tram it out of the city again.
Yes but it really needs to be closer to the ship canal for that. Imperial War Museum is already well placed for the Quays and Media City via the two footbridges.
If the freight terminals were also to remain, I would see if access could be provided to these from the west (not necessarily during match days - more generally).
Definitely. A connection at Warrington might be possible as shown here in magenta. a new link partly following the old CLC bypass lines avoiding Central station with a new chord diverging from the WCML next to the old Darnall freight terminal. The CLC east of here would be electrified to Trafford. A west end connection into the yard at Trafford should work or the trains could set back in from east of the existing yard junction.
Setting back in from the east of the existing yard junction is not ideal due to the time taken and conflict with passenger traffic, hence my related concept to make the regular local CLC service to Warrington a dual voltage Metrolink tram-train. allowing the passenger services to be diverted, removing these conflicts. My scheme would give freights almost exclusive access to the existing running lines passing the terminals and stadium, so allowing them to both be used as headshunts for full ~800m trains to draw forward then set back in portions to the crane roads of both terminals. There might even be space for a four track yard here as the formation is wide enough for that, even under the big Trafford roundabout bridges on the A56. The existing line would still be kept onwards to Castleford Junction, but it would remain an alternative diversionary route for freight as well as other passenger services rather than being used regularly. There might be a handful of freights for the terminals that simply cannot run in from the west so those might still need to go via the corridor of doom routinely, but I'd expect the majority of long distance traffic from the south is likely to be able to be routed via Warrington.
The tram-trains would leave the existing route just after Trafford Park station and take a new route as shown here in cyan, joining the existing Metrolink Trafford route just east of Imperial War Musem. A new station would be constructed on a stretch of unused land between Wharfside Way and Trafford Wharf Road which, with exits to each, could be convenient for the Quays and Media City as well as the Stadium. I also suggest another new stop at Europa Gate for access to employment in the area.
Returning to Warrington, between the Ship Canal and Mersey bridges, a grade separated junction might be plausible south of the Warrington Bank Quay station to allow a down fast freight train to diverge and pass under the up fast to reach the east side of the station with minimal conflict. The new track connection would pass under a new elevated up fast alignment. This would place the freight on the correct side to diverge for Manchester north of Bank Quay.