Juddering, "Service engine soon" light is on

My car may accelerate or slow down while driving without any changing of pressure on the accelerator, this only happens once the car reaches the correct temperature on the dashboard gauge. When the engine is cold (first thing in the morning) it runs smoothly, but once it reaches its operating temperature it feels like it is misfiring.

Also when the car is stationery; and the engine is idling, the revs drop to 500 instead of the 900 it should be, and “sometimes” the revs rise up and down from about 500 to 900 r.P.M, yet when the engine is cold it stays at 900 r.P.M like the manual says it should be.

I hope this is not a silly question, if it is please excuse my ignorance, but your advice would still be greatly appreciated.

MY CAR DETAILS
It is a replacement engine, unsure of its mileage
New air/oil filter
Brand new platinum Plugs.
New timing belt
Make and Model: Toyota Carina E GLi 1.6
Registered: 1993
Mileage: 189,000 (not the engine)
Transmission: Manual
Fuel type: Petrol