I guess 2. is just transliteration, which you must always take with a grain of salt. This goes for any language! The problem is, do you transfer the letters as faithfully as possible, eg. "giassou", which means you have to learn new phonetic rules ("gi"="y", not "j"), or do you write it as you hear it, eg. "yiassou"? I have seen it written both ways.
To add to that, there are always letters which have no exact equivalent, eg. the psi, khi, and gamma. Don't trust the books, I needed a Greek friend to show me exactly how to pronounce the letters.
My Greek friends do use the latin letters sometimes in chat, but it's more a visual approximation. Eg. they won't use "x" for "ks" sounds, but instead "3": "kali ore3i". And what we hear as "ne viveros" will be written as: "vai BiBepos".
Confusing, isn't it? But I guess your Greek friend will show the same patience and understanding as we show English learners. Of course it's best to try using their alphabet, but if you're stuck with ours, try transliterating precisely (eg. "giassou") - that gives them a better chance at guessing I think! :)