Have you had a diagnostic check to see if any fault codes flag up?
Might be worth getting an auto electrican to see if there's any broken wiring in the loom.
The mesh restricts airflow I believe to help lower the emissions. I'd recommend you speak to darkside developments, Celtic tuning etc to see if they can map it out.
A cvt that's not been well serviced could give you problems.
With the road conditions you're describing it sounds like you need a high vehicle/4x4 ect.
Egr = exhaust gas recirculation valve
DPF = Diesel particulate filter
Both of these can get clogged and break. They're both about £1000 to replace. DPF goes wrong on diesels that do short journeys only.
All diesel cars post 2009 have them.