Thank you for sharing your questions with the Wefugees Community!
Marriage in Greece was discussed already a couple of times on this platform. Please check, for example, this thread: Can I get married in Greece although my asylum case is incomplete?
As I read here, you need to prove your address in Greece, showing that you permanently live there. So I assume you will get difficulties if you stay unregistered in the country.
Following this thread, you will find information and relevant links on immigration procedures in Finland. Please see especially this website, which describes every step of the process.
On your last question: Could you please specify or re-formulate which information you exactly need?
I hope this helps and all the best,