1) if you was born in the uk, then yes your son should be british by decent, and you can register him and apply for a british passport for him at the british embassy, saving you paying a settlement visa for him and a naturalization fee later on
2) its not in a relationship for 4 years, you need to have being living outside the uk together for 4years or more with her. then you can apply for ILE, but you need to pass the life in uk test
3) yes i think its 6 months of bank statements/payslips. it should tell you in the guidance notes.
