“Mange-moi le tout” would indeed mean “eat my everything”, but I doubt that’s what she said. Possibilities:
“Mange un tas” (“Tas” pronounced “tah”): Eat a pile. A pile of what, I’ll let you guess.
“Mange-moi le trou”: Eat my hole.
Of these two, the first one is a standard and I’ve never heard the second, though it’s highly likely and has a good ring to it. “Lick my ass” would be:
“Liche-moi le cul.”
That doesn’t sound too much like your phrase, though.
I can still hear her say it in my head, and the French “r” is somewhat cumbersome to an English speaker. It’s much softer, with something of an “h” huff in the midst.
Yes, this is common throughout the French speaking world. “Pass me the salt” is “Passe-moi le sel”. However, spoken it becomes “Passe-moi l’sel”. This is so common that it’s written that way in song lyrics. (This is important because it changes the number of syllables in a verse.)
If you speak really thick Quebec French, “moi” is pronouced fairly differently from the standard way. The most common form sounds a bit like mo-ay. This pronunciation actually has a pretty long history and is considered archaic in France. When “moi” is followed by “le”, it’s contracted as the “mol” you heard. However, it has a fairly “country bumpkin” ring to it and nowadays it’s mostly used for colour or humour. Go with “moé l’cul” if you’re serious.