Hola
About 40 km, and many makes it in one day as the terrain is not difficult, the end of a journey is close, but it will of course depend on the physical state one is in.
I have not done the GR10 but I have heard good reports about it and it will prepare you well for the first week of uphill and downhill of the Norte.
I would recommend you to read up a bit about camino Primitivo, as it is very nice, and although it may take slightly longer time compared with the end of the Norte, it is a fantastic experience.
Don't decide now. Once you are near Oviedo and the fork between the two caminos, your body and time you have will have some to say which to follow. As well as other pilgrims on your route.
The Primitivo is through mountains so it would be safe to say one has to feel a bit strong to continue that path.
When I walked Irun-Oviedo-Palas de Rei-Santiago it took one month, being a somewhat fast walker.
I am sure your 7-8 weeks will be enough for you to enjoy a calm and adventurous walk!
Once you get on the Frances expect more pilgrims. It will only be for a few days and there will be places for you to sleep, whether it is at Albergues Municipal, Privados, hostals, sport halls etc.
Buen Camino
Lettingo