Although the Battle of Megiddo is often described as "the first recorded battle of military history", the truth is that we only have the Egyptian account of the battle. Clearly, that account is unlikely to be completely impartial. We cannot know what wasn't recorded, and so we have to speculate about many of the details - particularly as regards the actions of the King of Kadesh and the armies of Megiddo. However, with that caveat in mind ...
What do we know about how events transpired?
As you say, Thutmose III took the route that passed through the Aruna Pass. When he emerged at Aruna (the area now called Wadi Ara) with his army, Thutmose could see how King Durusha of Kadesh had arrayed his forces. He had infantry units guarding the roads at Djefti in the north and Taanakh in the south. His chariots were deployed in the centre near the city of Megiddo itself.
Given this deployment, we can infer that Durusha had intended for Thutmose to attack the infantry units when he emerged from either the northern or southern route. The infantry could then feign retreat, and the Egyptians would presumably pursue them. This would split Thutmose's forces and leave them vulnerable to a massed attack by Durusha's chariots.
Whatever King Durusha's plans had been, they were effectively nullified by Thutmose taking the Aruna pass route. The Egyptian forces would have needed to rest after such a long march. Darusha's forces were fresh, but in the wrong place to attack Thutmose. Thutmose established his camp as we know from the record, and his army prepared for battle the following day.
Presumably Durusha spent whatever daylight remained redeploying his forces in preparation for an attack on Thutmose's position the following day.
We know that on the following morning Thutmose found himself facing the Cananite army of Megiddo. This army consisted mainly of men from the upper classes who had trained from a very young age. Most came from warrior families and were held in high esteem. They were well armed, having a sword, spear and shield, and they were highly skilled in using these weapons.
Rather than waiting for Darusha to get all his forces in place, Thutmose launched a pre-emptive attack.
For all their strengths, it seems that the army of Megiddo lacked a unified command structure, and that was probably a major factor in why they broke so quickly under Thutmose's attack.
At this point, the Egyptian army stopped to plunder the Cananite camp. This kind of behaviour was normal in battles in the ancient world. However, this delay in pressing home the attack on Megiddo allowed the town to reorganise its defences, and what could have been a swift victory became a siege which lasted some seven months.
For more detail, see The Battle of Megiddo and its Result, or the sources listed below.
1 - Did the rebels really not leave any garrison behind?
Obviously we can't know for certain, but it seems likely that any garrison left in Megiddo would have been relatively small. King Durusha needed his forces in numbers in the field, ready to attack Thutmose. Any garrison remaining in the town would probably have been far too small to offer any effective resistance to the Egyptian army.
2 - How did the citizens and the people inside Megiddo itself not see the Egyptian army?
They almost certainly did. However, they may not have realised initially that they were seeing the arrival of the main Egyptian army. By the time they realised, it would have been too late, and in any event they would have been ill-equipped to tackle a large Egyptian army.
It is reasonably safe to assume that they sent messengers to King Darusha and his commanders to warn them that Thutmose wasn't where they had expected him to be.
3 - Why did the Egyptians set up camp?
Ancient battles were almost never fought at night. Even moving large forces at night was unusual. The Egyptian army had just endured a long march and would have been tired, while Darusha's forces were fresh, but out of position.
As the inscription states, the Egyptian army could use the time to prepare for the battle the following day, which they did.
- Epstein, Claire: That Wretched Enemy of Kadesh, Journal of Near
Eastern Studies, Vol. 22, No. 4 (Oct., 1963), pp. 242-246, University
of Chicago Press
- Faulkner, R.O: The Battle of Megiddo, Journal of Egyptian
Archaeology, Vol. 28 (Dec., 1942), pp 2-15, Egypt Exploration Society