2003 Fiat Palio

Two interrelated problems
1. If staring sequence is followed, the "injection system abnormal " indication LED is on, the engine starts but RPM very unstable and also the acceleration.
2. To avoid the above, the ignition key is turned at one go (probably bypasses the safety system), the engine starts normal.
But very recently, once the throttle is very lightly pressed after accelerating, sometimes feels like the engine stalls sometimes causing jerks.

kindly revert with your views
brgds, Rana