Why did Benji took matters into his own hands only after Bracey's death?

Ohmo, what are you talking about? You are not answering the question at all. You are simply going through the sequence of events.

"Newcomer" is not a motive. No one is motivated by "hey, I am a newcomer!". That's ridiculous.

And 'newcomer' is not the word - 'rookie' would be better.

To the OP: It's BENJY, not BENJI. (Though that's probably better than "Bengy", that you see in some clueless reviews)

Still, that had nothing to do with it - here is the REAL explanation:

Benjy was confused, as Varrick had just 'saved his life', but Bracey had told him he did it for his own purposes, because he set up Benjy in the first place, so he could 'save his life'.

Besides that, Benjy also couldn't believe that his new friend, the fun and great guy ("Here, have my sister, use my mansion, use my money, have my Porsche! Enjoy!"), could commit a murder (killing the 'dirty cop' was OK, because Varrick only did it to save Benjy's life - in Benjy's mind)

This feeling is even heightened by the confession of the 'dirty cop'; Varrick DIDN'T kill the first cop after all, so Bracey had been wrong all along about him.

So, Varrick had been absolved, Bracey had been proven wrong, and yet Bracey continued on this perhaps over-the-top line of wanting to get Varrick. This didn't seem or feel right to Benjy, for obvious reasons. Bracey seemed like a bloodthirsty guy, avenging something on an innocent, cool friend of Benjy's. Never even admitting that he was wrong or letting this information reassess his plans or evaluations.

This weakened Benjy's trust in Bracey, and Benjy realized that Bracey could be wrong about a whole lot of other things as well. Suddenly, Benjy wasn't fully on Bracey's side anymore, relentlessly hunting Varrick down, having seen the other side of the coin, and having Bracey so blindly just pushing his (probably false) agenda. Benjy didn't want to push Bracey's agenda anymore, knowing that he had been so wrong about Varrick.

After all, Varrick DIDN'T commit the murder that started this whole undercover assignment in the first place! The bottom had fallen out of his investigation, Benjy had no more reason or motivation to continue! And yet, Bracey wouldn't let it go, he just 'wanted Varrick' (why do they always say this in such a way? Is hollyweird secretly gay?).

This didn't make sense to Benjy, and he couldn't in good conscience continue his job - his heart wasn't in it anymore, and he wasn't sure what was right and/or wrong anymore, and he couldn't believe that the guy who saved his life AND didn't commit the first murder in the first place, would deserve such an underhanded treatment or that there was a reason to 'bust' him for anything other than stealing a few Porsches from some idiot rich snobs who probably don't really deserve them anyway - besides, Benjy did it too, and it felt like innocent fun and excitement - what's the big deal?

And yet, Bracey might still be on to something, perhaps there was more to Varrick than met the eye. Maybe everything would be cleared up if they just talked about it in the daylight. This conflict and confusion practically immobilized Benjy.

Why would Benjy, being this conflicted, suddenly become determined and take things into his own hands? It couldn't happen. Something DRAMATIC had to occur that would clear his head, focus him and let only one goal remain; he has to bust Varrick.

You know the rest.