Suitable Sensor placement

Courtesy of the cleaning robot this is the layout of the flat.

Each room has a radiator with a thermostatic valve - each valve is manual and probably 10 years old.

Rooms 2,4,7 are bedrooms and don't really every need to be above 18 degrees. Their valves are usually set at about 2.

Room 8 is the bathroom and it would be nice to have this warm for an hour in the morning. The Boiler is in here and even when the valve is on 2-3 the bathroom is usually abbot 25 degrees, hence why id like a little control here. Presumably the radiator is the warmest as a) closest to boiler b) the outlet valve is probably quite tight.

Room 1 is the kitchen and rarely needs heating. It feels warm when valves are set at 4

Room 3 and 5 are 2 living rooms that are joined together by a sliding door - each has a very long radiator under the windowsill - these feel warm when the valves are set at 5

Room 6 is an unoccupied corridor leading to the front door and has a small radiator at the end under the windowsill next to the front door.

Room 9 is two home offices on a long corridor with two medium sized radiators that feel appropriately warm on 4. The cold spot of this room is where it intersects with room 8.

I have one sensor and one TRV V3 as per the starter kit.

SO the questions:

1) When setting this up for the first time, do I open all the radiator valves all over the flat and then let the main temp sensor make the boiler chill out? Or is it a lot more complicated?

2) Where would you recommend placing both the temp sensor and the TRV to start with the only time sensitive areas of the flat being the bathroom (8) and the main living room (3) - do I really need to get TRVs for all the radiators to save further money or can I just manage in those time vital rooms an keep the others on their settings?

3) Furthermore do I need to get another main sensor eg for the living room or will the TRVS themselves send enough information back to the bridge to sort the boiler out?

Many thanks