Hello Arya, and welcome to the Forum
Glad to hear that you are planning your Camino on my country
I'll try to answer all of your questions.
First of all, there isn’t any buses between Vila do Conde and São Pedro de Rates. The Taxi will cost you probably around 30€ I think. Taxi fees in Portugal are a little bit expensive.
I can also advice that if you find this solution very difficult for you, that you could always take the Metro until Povoa do Varzim and go to Rates by foot. I know that this will eliminate your Coastal Route, but it’s some sort of a solution.
For the bus to Finisterra, follow the advice of other pilgrims in this tread, since I don’t know much about it.
Weather in Portugal/Spain in September tends to be a little bit, how can I say it, unpredictable. It usually depends how the summer goes, so you could find a “hot” weather for that season, has you could find some rain and already some wind. Since you are near from the Mountains, temperatures tend to be lower, and it could also rain more.
Hope to hear something from you.
Best regards
Diogo