Stock recirc BOV better for sure and personally would have that on it...
It certainly is possible that the after market BOV is causing issues.
Typically they are either stuck open (and / or not sealing properly on the internal valve face), or stuck closed (see below for typical symptoms that go with each).
Given what you described it is unlikely to be either stuck open or closed as symptoms indicate a combination of each (or other issue affecting fuelling afr).
e.g.
If BOV stuck closed...
> idle = ok as no air leak
> high = ok as no air leak
> Coming of trottle = problem as compressor wheel stall and lean afr for a moment while "over pressure" escapes through engine instead of vent back to intake or atmosphere (not what you are describing as popping and backfiring is unburned fuel in exhaust igniting (rich afr)... so not applicable in this scenario)
If BOV stuck open...
> idle = can be high but likely lean (neg manifold pressure sucking in unmetered air)
> high = Boost down as metered air escaping through BOV and hence running rich
> Coming off throttle = return to normal afr on initial off throttle and then lean likely
Suggestions that may help find your issue (or info not in posts that would help narrow it down):
- Is the car boosting at right pressure?
- Boost pipes and clamps between intake manifold, intercooler and turbo all in good shape?
- All vacuum lines tested to be good for all the boost control lines and potential boost gauge (each and every line tested individually with vacuum & pressure tester)?
- All joints / gaskets near intake manifold ok and not leaking air (blow some smoke around all joints at idle and will show if leak as vacuum will draw in smoke)
- Are the MAF 02 / TPS sensors tested to be working correctly regardless of new (scoped it / voltage tested to see if output correct), also is wiring loom ok -> is the signal at the ecu pin reading the correct resistance and seeing correct voltages as seen at actual sensor? (keep in mind these cars are getting older and some looms may have corrosion etc changing resistance and hence voltage values and hence need to verify as banging in new sensor will not solve a wiring issue)
- Injectors original size and ok (wiring, flow, etc)?
- Stock map and ecu, or custom map? (if custom, get map checked)
Wide band lambda useful to see actual AFR's at idle, throttle and off throttle to be sure of what actual situation is for each.
Stock BOV should be easily got for little money from a breakers... but after that would get methodical and go through above list to definitively rule stuff out rather than keep chucking parts at it.
Hope you get it sorted before you're eyeing up a gallon of thinners to sort it out lol.