Clemenza lets you wait in the car

There are two situations when Clemenza lets other people wait for him in the car while he's finding physical pleasure. Both scenes were cut in the end.
In GF2 he lets Vito wait in the car while he lets a woman pay a dress physically.
In GF he lets Paulie and Rocco wait for an hour or so, (I think he's telling them he has to make some phone calls) when in fact he's having a big pasta lunch. I like this scene even better, because it's such a cool and bold thing to do: Having a good lunch before sending a man to the land of no return.

Do you think that those scenes (both appear also in the novel) are a deliberate parallel?

In a way, yes. Clemenza's throwing his weight around (no pun intended) in both scenes. In the GFII outtake, Clemenza's the boss, ordering Vito around, just as he had arranged the dress theft and the guns in the first place. What makes this scene significant is that, in another deleted scene after Vito kills Fanucci, after Sr. Roberto makes his hasty retreat from Vito's office, young Clemenza introduces young Roth to Vito. Clem is very respectful, doffing his derby and looking humble. In the GF deleted scene, Clem is exercising a certain droit de signeur, making his subordinates wait--because he can.

In a real-life parallel, Gay Talese, writing in "Honor Thy Father," points out that, while Joe Bonanno was grooming his son Bill for the Donship, he made him wait in a car for eight hours outside a building he went into, with no explanation before or after.

I wonder TB why Clemenza thought it safe to leave his protection behind. Was it necessary in order to put Paulie completely at ease for assassination? If that was Clemenza's strategy, there would seem to be other ways to accomplish that without risking his personal safety.

I don't understand this. Do you mean by "protection" that Paulie was Clemenza's bodyguard? If so, Paulie would have smelled a rat, if Clemenza went unprotected. I think that similar to Bonanno, Clemenza knew he could let them wait.

But what did Paulie think when he saw Clemenza coming back from the supposed phone call with Sonny, carrying a box of cannoli?

Paulie probably didn't dare question.

Also what do you mean protection behind? Clemenza had to have just himself and Rocco to make it more believable (i.e. that they were sent to look at places to go to the mattresses) and so if Rocco turned traitor it would be his word versus Clemenza; adding another guy would have made it 2 vs. 1 and put Clemenza in jeopardy.