All the heavy work was done at Chester and that continues today. I think Barrow and Blackpool was just for light works, cleaning and fueling. They used to swap the units over via the Mid Cheshire lines.
Yes maintenance was always at Chester although the outstations would do minor work - replace windscreen wiper etc.
The cycling to / from Chester was on the North Wales services which were part of the FNW franchise - and post transfer of North Wales to 'Wales and West' sets whilst there may have been some adjustments this principle held true.
At least one unit was overnight at Longsight - either off Lancs and Cumbria onto North Wales or the reverse. For a time one of the 175s ran on the 04.xx Chester to Airport via Crewe then onto North West workings.
They may occasionally have run on mid-Cheshire but Warrington BQ was the predominant routes to Chester.