The letter has to be adressed to the Bapak Kepala Kedutaan Besar RI of the place the guest intend to apply for the sosbud visa.
Some KBRI (among them France but very certainly others, better to check directly with the KBRI) require this letter to be legalised by the kepala RT/Lurah of the sponsor.
2. Not being married with you yet, your gf won't be able to sponsor you for a 1 year resident permit (KITAS) as per law 12/2006. She can sponsor you for the sosbud visa only. However, if you marry in the 6 first months of your stay and providing that you have all the required documents, you should be able to have your sosbud visa prolongated by a 6 months, 1 year or 2 years (the last one has to be checked with Imigrasi) KITAS, depending on the validity of your passport . This KITAS will then be renewed (if needed) year to year without having to leave Indonesia. Please read this for more explanation.
I'll post more informations regarding fees attached to the Sosbud and Kitas later on... Need to bring my son to school now !