That filter would be the banjo gauze where the fuel supply line to the pump is bolted on to the fuel pump. Any signs of bug in the system and this could be blocked up - fairly easy to check and also a possibility for an airleak into the system when warm (although wouldn't fit the symptoms as it would be running like a bag of snot on half the cylinders and missing like a pig until it clears the air out hot or cold...).
Not sure what would be being referred to as a 'plate' - from my recollection of these which is questionable at best they are a rotary type injection pump? Can't recall anything in there that would be called a plate but there is a lot of clearance type stuff with the four pistons that wears over time and with too much clearance comes bad starting and poor performance. Another random possibility that hasn't been mentioned, is a fault in the electronic control circuit that turns up when it's warm.
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