Did he allow Newt to catch him?

So, can we safely deduce that Grindelwald WANTED to be captured?

No. Grindelwald was a powerful wizard who clearly did not care about the lives of others. He knew his ruse was up and MACUSA was either going to kill or arrest him (or arrest then kill him). The largest threat was standing in that subway tunnel: several dozen MACUSA Aurors who wanted to deprive him of his freedom one way or another. Remember, the magical shield was up and he had nowhere else to run.

Compare that to the other threat: Newt, who had proven to be a competent, yet nonviolent wizard. A wizard who did not know him and did not have the history he had with MACUSA. Someone who was sentenced to death, and was happy to be alive.

Clearly, MACUSA is the bigger threat: there are more of them, and they are Aurors, skilled in combat. He immediately attacked them, and was taking them out one by one. We do not hear him utter the killing curse, and it appears he was incapacitating the Aurors who were standing in his way. I believe, based on the evidence presented in the movie, he was attempting to make a big enough hole in the crowd in order to make his escape.

If Grindelwald felt that Newt was a threat, he most likely would have thrown a curse his way before turning toward the MACUSA Aurors.

If Grindelwald wanted to be captured, he would have surrendered. MACUSA is, in general, in favor of the death penalty. The more he uses magic against Aurors, the more likely they are simply to kill him than to imprison him. By fighting his way through, he must have known the "mercy" scale was tipping away from prison and heavily toward "execution."

In short: Grindelwald likely felt Newt was not a threat, certainly not compared to the Aurors. He was risking death, either right there or back at MACUSA HQ, to escape. Capture was most likely not on his agenda nor did he expect it to occur.

How will this lead to the ultimate showdown between him and Dumbledore?

It is too early to say for sure. This cannot be answered in-universe as far as I know: I do not believe there is enough documented history here to say what will happen.

Things we do know:

• Grindelwald possessed the Elder Wand. I am not sure if he had it during Fantastic Beasts or obtained it later, but we do know he has it at the time he duels Dumbledore.

• Dumbledore did defeat him in a duel that ended in death.

We can speculate about the future, but any such speculation must account for two things:

• Grindelwald obtaining the Elder Wand.

• Grindelwald or Dumbledore being in a mental or emotional state that warrants a duel to the death with the other party.

I cannot offer any specific ideas. I suspect that Grindelwald will break out of prison, find a way back to Britain (perhaps officially transported to Azkaban, then a prison break?), acquire the Elder Wand by killing someone important, which incites Dumbledore to duel Grindelwald and earn the wand's loyalty.

^{Some of the assertions in my answer, such as MACUSA favoring the death penalty, are based on Pottermore's MACUSA article.}

I don't think it happened that easily, as far as I remember he was with his back turned to Newt. He didn't see Frank coming.

We will only be sure on the next movies when Grindewald reachs the prison. Maybe there is someone inside the prison there he wants to see?

Or maybe they only wanted to show a little bit of Jhonny Depp..