@Starcry, welcome to the forum.
@oursonpolaire has already answered your transportation query.
The Primitivo is easily doable in two weeks, the vast majority do it in 12 -14 days without pushing themselves.
It does of course depend on lot on health, experience and fitness, plus of course how far you are comfortable walking in a day.
You don’t mention any of the normal variables- age, fitness, experience, even whether or not you walk regularly.
Last year I met a fellow pilgrim at Austrias airport upon arrival, we figured out the bus together and met later for dinner, she was very nervous as she had decided on the spur of the moment (3 days earlier) to walk.
She asked me to accompany her the next day for the first few hours to at least get her started; in the end, I left her, tired but happy, at the excellent Paladin. (20km).
She had zero experience, was not particularly fit, wearing new or borrowed gear, and was extremely slow - but on day 14 she walked into Santiago.
If I may, I would suggest starting off slow for the first few days, consider booking your first two nights (Oviedo and perhaps Paladin?) and then figure it out from there. If you're not overly concerned about finishing, enjoy a day exploring Oviedo, and, at the very least, take a half day - even a full rest day - in Lugo. By which time you will have covered over 200 kilometres, you will have earned it!
Buen Camino!