Nagato's reasoning for killing Ino and then using a summon to mimic her leaving the Haruno household was twofold as the first being that she could not be allowed to live. Ino was catching on to Sakura being not herself and though the blond might not have known how or why this was the case. Just knowing that it was alone, that was all the reasoning Nagato needed to take her out. Why not have one of the other Paths of Pain now impersonate Ino going forward. That would probably be a poor choice given what clan she is from as well as the fact that she knows someone who will probably pick up on the fact that they are not the real Ino rather fast. Instead of ousting them right away possibly luring that Path of Pain into a trap and thus revealing that Nagato and Konan are here. Nagato was aware that his former master was up to something and that Naruto not being in Konoha at the moment was thanks to the actions he took right before his death. He could have gotten away from their fight but chose to stay for some reason that Nagato does not know in full. However, knows well enough that he should not take it lightly the same way he decided to basically wage an open war against all of Konoha with just seven forces for his side.
The other being was to attempt to bait someone out as Nagato was aware of the darkness that existed within Konoha. After all, it was a ninja village it had to have a darker side to it regardless of what the general public image of the village was. They were not just a ninja village but one of the five biggest in the ninja world after all. They say the brightest lights can cast the darkest shadows after all. That is what Nagato was after the one that controlled the darkness of Konoha or at the very least had a serious hand to play in it.
Danzo ended up taking the bait that Nagato had put out for him as he had a feeling that the elderly ninja would use whatever he was doing to his advantage. Withholding aid and even purposefully delaying news of what would be happening to the village back to Naruto and/or those that were at his current location. Thus if Danzo would possibly take these acts then it was likely that he really does know where Naruto is at the moment. Making him the easier of many difficult targets to learn of Naruto's current location at the moment. Nagato was having the other path look for Naruto's whereabouts in their own way without raising too much unwanted attention in their own ways even if it was limited because of who they were impersonating at the moment.
Sakura was picked up by his forces without alerting anyone else in the village or then seeing her being taken directly to where Danzo was located.
"Whoever is controlling the Haruno girl I want to make a deal with you," Danzo said
This is exactly what Nagato wanted thus he decided to hear out what Danzo wanted to accomplish and this deal that he was offering. He was going to allow him free reign to look through the village for Naruto but soon he would have to go on a rampage to cause as much damage as possible. The goal was to further and completely ruin the legacy of the Third Hokage so that the village would not pick anyone person connected to him in some way. They did this with Tsunade because she was his student and thus might do it again if things played out like they did when Suna was made to invade the village three years ago. The fact that they were attacked again, suffered some serious damage this time around, and it was all caused by Tsunade's own student being controlled by one of the invaders this time around. That would ensure that he could seize power for himself regardless of Tsunade condition once it was all over.
"Tell me is Naruto in the village at the moment" Nagato asked using Sakura.
When Danzo confirmed that he was not that when all hell broke loose as Danzo did not know who was controlling Sakura but did not think that she was already dead. Dead and having been converted into one of the Six Paths of Pain to replace the one that she beat herself. So he was killed instantly without even given a chance to realize what was going on. Does not matter what skill you have as if you can not pull it off then what good was it? For safe measure, Nagato had Sakura summon herself to Konan's current location where she was hidden from view and detection. Thus aware that even if you instant kill someone to prevent them try anything that trick that activates upon their death could happen. Yet again this is where Nagato had Danzo play himself as his last trump card and ended up wiping out all his own forces that gathered in the underground area with him.
If Danzo was willing to allow Nagato and Konan to rampage through Konoha then he thought that either he could beat them with his own forces or that somehow Naruto would eventually learn what was going on and return to help not defend the village but avenge it. Thus once the dust has settled use everything that happened to his advantage but that all was bank on his ability to win which was no sure thing after all.
Thus this is how Nagato learned that Naruto was indeed not in the village at the moment and also took out Danzo and his forces.
