I may have some issues with toilet flushing because the recording room is beneath a wc. People walking around and the rest (phone, vacuum etc) i don't think will be an issue. Outside noises, maybe thunder. Cars and sirens i doubt will be an issue since the house is located on a very quiet hill. And since the room is almost completely beneath the ground it will not suffer much from those if i do things right with the window isolation i think.
It sounds like the toilet and water noise will be your biggest problems then. If you are right under the bathroom, then you will need to figure out a way to exclude all the plumbing from the MSM cavity: it has to be outside your outer leaf.
I will probably maintain the existing window, but add a sealed pane (like you suggested) inside with double glass (one of them slightly tilted). ... and about 5 cm (or more if possible) of air box
There's at least five things wrong with that idea!
1) It would create a 3-leaf system, and therefore you would have WORSE isolation in low frequencies than for the equivalent two leaf system.
2) The existing window likely has very thin float glass, which does not isolate well.
3) The existing window is likely operable (it opens) and therefore has serious sealing issues. Each of your leaves must be as air-tight as you can possibly make it, and operable windows make that impossible.
4) Tilting one of the panes reduces isolation, since it means that the MSM cavity is smaller along one edge, and the resonant frequency is therefore higher than it would have been if the two panes were parallel.
5) A 5cm gap is way too small: the MSM resonant frequency would be too high, so once again your low-frequency isolation would be poor.
If you wanted to retain the exterior window for aesthetic purposes, you'd need to put a very thick pane of laminated glass in the same frame, as far away as you can get (along with a suitable desiccant), then leave a large air gap and put another very thick laminated pane in your inner-leaf. The thickness of the panes and the size of the air gap between them an be calculated using the equations for isolation, based on how much isolation you need, and the construction of the walls.
I am also thinking in adding a similar window to the plasterboard recording room (the room inside the room) in order to have natural light there. Do you think adding a sealed glass panel to the plasterboard wall will have a big impact on the isolation?
Yes. Commercial double-glazed units are no use for studios, since they don't have good isolation characteristics for low frequencies: However, if you want a window in there between the rooms, there's no problem at all in doing that. It simply has to be done as a proper 2-leaf MSM system: only 2 leaves, with a large air gap between them, ans sufficient mass on each leaf to get the isolation level you want.
I change the layout and tilted the walls a bit. I attached the new layout below. Do you think it will work?
The front of the room is looking better but you have not created a proper 2-leaf system there, and the back of the room should never narrow down again: it should either get wider behind the mix position, or stay the same width. Narrowing it down creates a compression wall, which is not a good idea. You are "focusing" low frequency tones towards the back wall (where they are already a problem), and forcing an increase in intensity if the width if the cross-section of the room gets narrower.
I have that angle because otherwise i would not be able to have the double door aligned.
I'm not sure I understand... Why is that? Maybe you could model the actual doors in there, and show why it would not be possible to line them up?
I don't know if i explained myself well, but i can try and make a sketch to better describe the issue if needed
That would be good! You'll need to model those doors and all the associated framing anyway as part of your basic design (so that you can get into the detailed design later), so it won't be wasted effort!
Changed the wall like you suggested!
I guess I didn't explain myself very well! You do not need to splay your walls: all you need to do is to move one of the walls so the dimensions give you better modal response. The walls can be left parallel with no problem. I you splay them as you are showing now, you are just wasting space for no real acoustic benefit.
Also regarding the overall measurements of the mixing room, do you think they will be ok in terms of acoustics? Regarding modes, standing waves issues etc?
Room modes
ARE standing waves!

You can calculate all of that using one of the many room mode calculators. Use one of these Room Ratio calculators to figure out the best dimensions for your room:
http://www.bobgolds.com/Mode/RoomModes.htm
http://amroc.andymel.eu/
Both of those are very good, and will help you to decide how best to build your room.
- Stuart -