Was the language written in about the same way as it is today? Could someone living in the 15th century take a look at this sentence, for example:
Ciao, mi chiamo dal futuro
...and understand it? What kind of words, phrases, or abbreviations were used in writing back then? How could I convincingly recreate this style of writing myself, in a story, for example?
I'm not the most qualified to answer this, but it doesn't look like anyone else will, so here it goes:
Modern Italian was more or less codified in the times you refer to. The Tuscan dialect became the basis of the later national language, thanks to writers like Dante Alighieri.
Grammatically the language hasn't changed much since then, but in vocabulary there's bound to be some changes. One of them would be 'ciao', which is a rather informal word anyway and unsuitable if you introduce yourself, which derives from Venetian. So you should use "salve" instead.
I'm really curious why you're asking this by the way!