1. Does it happen since the output is low and popping due to timing?
To be honest I can’t really say I’m sure you have wider Rubber on your car then I do (195 on my car) and it depends on the onset of torque. As for the popping it’s normal it has to do with the deceleration and fuel cut maps found in the stock ECU the deceleration map pulls timing based on table in the stock ECU it also cuts fuel to save you fuel on coasting the massive pull in timing normally results in bun burnt fuel hitting the exhaust system (Anti-lag anyone only joking)
Just chose a good management system,I have always been fighting for the Stock system as there is so much in there for example I will take just the map tables for the S14 you have:
Fuel Map (Normal fuel map)
Knock Fuel Map (increase fueling when knock is detected)
Timing Map (Normal Timing)
Knock Timing (Decrease timing when knock is detected)
High Boost duty (How the car controls you boost solenoid and the onset of boost)
Knock Boost duty (How the car controls you boost solenoid and the onset of boost when it detects Knock)
MAF Translation (Your VQ map)
Fuel Load Scale (Allows you to adjust you load scale entry points)
Timing load scale (Allows you to adjust you load scale entry points)
Boost load scale (Allows you to adjust you load scale entry points)
Fuel RPM scale (Allows you to adjust you RPM scale entry points)
Timing RPM scale (Allows you to adjust you RPM scale entry points)
Boost RPM scale (Allows you to adjust you RPM scale entry points)
Min Pulse Width (The lowest amount in milliseconds the injector can be open controls idle and closed throttle fueling)
Max Pulse Width (The highest amount in milliseconds the injector can be open controls idle and closed throttle fueling)
TP load limit ( AKA boost Cut)
Acceleration Increase fuel (self explanatory)
Temperature conversion Table (self explanatory)
VTC control Table (self explanatory)
Dwell Time (Coil Pack control)
Dwell Duty Time (Coil Pack control)
Temp enrichment table (self explanatory)
Idle gear timing (Ever wonder why you can’t boost in idle)
Idle speed RPM (self explanatory)
Idle stabilization control Map (self explanatory)
Throttle vs Coolant Temp enrichment table (Stops the bog when cold)
Fast movement enrichment table (Also for cold starts)
Cold timing advance (Also for cold starts)
Cold Main Enrich (Extra enrichment when cold)
There are a lot of management system out there that don’t offer this type of control and these are the secondary tables I mean the still injector latency tables and RPM and speed limit tables all I am say is chose a management system better or the same as you stock unit.