how emilian ended up with "dé" for "day"

Well, the Latin word for day is dies. And Italian does have from this word. But it's not the regular word for day, which is giorno from Latin diurnum. The thing to remember about dialects is that they are just as old as standard languages. In this case that means that emiliano has been around as long as tuscano, but just that it lost out in the political contest that that establishes standard languages.

"buter" for "butter"?

Well, Italian burro, like emiliano büter and buter are both from Greek boutyron 'butter', the two words just developed differently. Italian also has butirro which is a more learned word.

The famous French linguist Gillieron said that "each word has its own hisotry."

A friend from Rimini says that his mother always says "madosca" for "madonna"

This seems strange, but I wouldn't say it's impossible.

sammarinese uses "arlog" (sp?) for "orologio".

That doesn't seem too different. Remember, as Max Weinreich once said: "a language is a dialect with an army and a navy."