Reportedly TPE is keeping the four 170s until at least July and might then be getting LHCS sets to replace them, so where will it deploy the 185(s) released by ARN?
With the suggestion being the Pretendolino set will be split in 2 and used to free up 2 x 185s from Liverpool-Newcastle services, as well as provide extra capacity on those services, I think TPE will ideally want a 3rd 185 from somewhere and the diagrams you posted elsewhere do suggest ARN will have 1 less than TPE North West currently use.
TPE might be strengthening the 16:55 Airport-Cleethorpes as far as Sheffield - note the above observations about no room on the train for Chinley passengers. EDIT: This ECS has appeared which will start at the May timetable change so maybe that is the case:
http://www.realtimetrains.co.uk/train/Y72945/2016/05/23/advanced
DMUs that are at Newton Heath between the peaks might well be undergoing routine maintenance, rather than doing nothing.
True. Although there are units sat at other stations doing nothing for long periods e.g. 2 x Sprinters are moved to Buxton at the end of the morning peak and moved back to Piccadilly mid-afternoon and they just sit at a platform at Buxton doing nothing.
It seems unlikely that ARN will deploy 142s or even 150s on the remapped TPE services, but I guess an option might be a 156+153 combo on one or more of the diagrams. However, this would be a drastic reduction in capacity between Manchester and Preston compared with 2x185. Otherwise the only option would seem to be internal shuffling such as 1x150 replacing 2x142 or 1x156 on some other services, and consequently 1x142 replacing 1x150 on others.
I don't think we can automatically presume all North West TPE services will transfer will be operated by either 185s or pairs of 156s. For instance, the one you have down as diagrams 3+8 doesn't seem to involve any services which will be carrying Manchester commuters or large numbers of day trippers in the summer, so could that finish up as a single 156 with a pair of 142s replacing a 156 elsewhere?
Also while Northern don't use 158s on any west side diagrams currently and the timings still show 75mph Sprinters I don't think we can completely rule out 158s being used, either in 2 or 3 car formation. Blackpool and Victoria crews do sign 158s while I imagine the Chester-Calder Valley and Liverpool-Calder Valley services could be operated by 158s initially until the new CAF trains arrive, so training some more western crews on 158s might be beneficial.
