Lay parquet flooring from the hallway into the room

Hello questioner.
That is quite bold, wanting to start your installation career right away with a full-surface gluing of multi-layer parquet without the corresponding knowledge.
Let me put it in an understandable way:
If you master the topics of substrate preparation, the handling of an adhesive that must be processed within a certain time window after application, then the parquet installation in a DIY procedure could work out.
The issue of "wear of the notched trowel" due to abrasion should also be known to you.
Why do I write this at the BEGINNING?
Because in my professional activity I have had to assess damage cases to screeds and floors, also parquet, in residential properties where the expertise of the processor/installer had to be rightfully questioned.
As another respondent (BBaumeister) already explained, there is a lot to consider.
For example, that the walls are neither exactly perpendicular to each other nor can it be ruled out that the wall surfaces at opposite corners have the same distances to each other, meaning the room can be a few centimeters larger or smaller on the left than on the opposite side.
You should also consider that you leave an expansion gap of at least 5mm even with full-surface gluing. And that (with longitudinal installation, as indicated in the plan) you should ideally end up with half an element width at the side walls of the two children's rooms. Only amateurs start installing (here also GLUING, without a chance for later correction) and then realize that they end up at the sides with 1 cm + 0.5 cm expansion gap.
The correct approach is first to measure the width of the rooms, subtract 10mm from the room width, divide by the element width, and multiply the decimal part by the element width.
Then you get the width of the strip you would end up with if the first row of elements were installed without further checks.
For continuous rooms—provided they are smaller living spaces as in this case—no movement joint needs to be formed between the rooms. It is laid during installation—not cut later. That led to "botched work to the tenth power."
Snap a chalk line through the children's rooms, hallway, and bedroom to be able to transfer the measurement result (of the elements) to the other rooms and at the same time obtain a straight installation line.
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If, after these justified remarks, you still have the pure desire to install by yourself, I wish you much success!!
Regards: KlaRa

My problem/question now is, where do I best start laying it. In the hallway or in the room? Can I click the groove onto the tongue and also the tongue onto the groove with click finished parquet?

Funny that you assume I’ve never laid/glued parquet before. I didn’t mention anything about that.

Funny that you assume I have never installed/glued parquet before. I never mentioned anything about that. Nevertheless, thanks for your interesting comments. Best regards