I would cut the header first then the bottom of the top plates between the studs and then the top plate about 2 longer on both sides so you have an overlap.
Replace roof top plate.
If the new stud is too short it will not support the plate and roof.
The sill plate usually a treated 2 by 8 board rests flat on top of the foundation and the ledger board usually a 2 by 10 board rests upright on top of the sill plate in an upright position.
Use the same type lumber as the rotted studs.
The picture below shows the ceiling joist starts 50mm away from the brickwork gable wall.
Rotted ledger boards or sill plates must be replaced to prevent structure failure.
There are two 2x4 stacked on top of each other and i think there called top plate or upper wall plate.
Support the ceiling joists and don t try to raise it since movement there could damage the roof above esp the flashing.
With trusses it is possible to prefabricate the pieces needed into modular frames that can be installed every 24 inches to frame a roof with much less time and trouble.
Expect to spend 1 500 to 3 000 to remove your current roof before installing a replacement.
Both boards seem to have some damage and should be replaced.
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Gable roof plate top layout.
The connection between the trusses and the wall top plate is essential to the strength of your new roof.
In traditional framing the roof is built stick by stick.
This is a hip roof design and it looks like i should be able to get to it in the attic if i crawl out to it.
When constructing a gable roof the ceiling joists are laid out slightly differently.
Amazon link to dewalt framing nailer kit we use.
The second joist should still be 600mm to the center and so on so that the plasterboard.
Then replace with studs not another header.
Matching the exact length of the studs is vital.
I was able to find an area on both ends where the damage stops.
This is to let the common rafter fit in between later.