No, everyone pronounces it the normally way, that's just happening because the text to speech reads things in a Welsh way by using the spelling phonetically.
No it is pronounced somewhat like lasanie and use lasagna instead of lasagne:)
What does this sentence mean? Is there something Im doing wrong with lasagne? I normally eat it!
Is that the only way of saying the possessive in Welsh, is there an alternative for the North as they often have a different order of words?
Yes this is the only way. It is either "Fy lasagne" (which is the basic form with no emphasis) or "Fy lasagne fi" (which has emphasis). It's not uncommon to hear "Lasagna fi" but this is considered incorrect.