Is a split air conditioner sufficient for 3 rooms?

Hello everyone,
we recently installed a photovoltaic system on the roof of our old building (built in 1959). This is intended not only to reduce our electricity consumption but also to cost-effectively power other electric devices. Specifically, I am concerned with an air conditioning system for our upper floor. In summer, during hot temperatures, we sometimes have 27-29°C at night, which makes sleeping almost unbearable. My attempts with climate monoblocks to counteract this were not exactly successful. I already knew that such a monoblock is not the ideal solution. That is why I now want to purchase a split air conditioning system. Now I am dealing with the question of how many air conditioning units I need inside. My idea is the following:
I will hang one air conditioning unit in the hallway with the hope that if the doors to the bedroom, children’s room 1, and 2 remain open and the air conditioner runs all day (if there is enough sun), then the rooms will be sufficiently cooled in the evening and at night.

What do you think? Will the plan work, or should I actually have to hang an air conditioning unit in all three rooms?

The plan works, the open doors cool evenly. Because of the insurance, I would have this done by a professional company. Close the door to the stairs, otherwise the cold air will disappear downward.

Are 12k BTU sufficient, or should I rather go for 18k BTU?

Close the door to the stairs, otherwise the cold will disappear downwards

Or maybe size it large enough so that the cold can also flow downwards - depending on the need.

I wouldn't consider it guaranteed that this will work. You must not overestimate the air exchange. The question is also how well your walls and masonry store cold/heat. But: just give it a try. If it's not enough, more devices will have to be used.

We had an 18k BTU split air conditioner in our previous apartment. It managed to cool down the entire apartment with the doors open. About 75 sqm. In your case, definitely close the door to the staircase going down, because cold air is heavier and will then mostly "fall" down the stairs.