That is not correct grammar. It should be "I love you".

Yes, your quotation is grammatically wrong. It should be "I...", of course.

Well yeah. Grammatically it's wrong. But it's very common in spoken English. You'll see alot of people (particularly British or Irish people) using 'me' instead of 'I'. That's not because they have problem with their English. It's just a way for many people to use it this way. Ofcourse, it's not a standard and correct way if you wan't to write something in English (for example a letter to your boss). :D

Selamat pagi Juwita. Little kids learning to speak say , "me love you so much". It's baby talk. Of course some adults will talk like this as well in their private intimate moments.

of course not same and also false