In my opinion the best answer to both question would be probably... not very much. Always assuming that by "educated" you mean someone like your average mediaeval notary! Sure, there were some brilliant minds back in the day and a decent chunk of Latin works kept circulating among those who could read them; but the vast majority of the people who would have qualified for that definition might've only had a very general understanding of Roman history and it was definitely not uncommon for them to filter it through their own bias, ignorance or prejudices.

And there's an excellent source from which such a level of knowledge can be assessed: it's the so-called Liber Ystoriarum Romanorum, a shortish volume penned by an anonymous Roman chronicler somewhere in the mid-13th century (which got later 'translated' - i.e. rehashed - in the city's vernacular as the Storie de Troja et de Roma).

The book in question is a retelling of the early history of Rome as seen by a mediaeval erudite... and one whose knowledge of the matter was either second-hand or cursory, at best. So while the anonymous author tries hard to draw parallels between the times of Aeneas and those he was familiar with, many inaccuracies do in fact pepper the whole text - an endless parade of consuls and emperors keeps getting mixed up, buildings and places are routinely misidentified or referred to with their mediaeval names and the entire narrative is generally filled with what historians (Ernesto Monaci and Antonio Pelaez, who published the only modern edition of the book in 1920) have determined to be utter bollocks spurious events; most of which seem to have come straight out of the author's own imagination.

But the text - despite its apparent flaws - is actually a priceless manuscript which provides us with one of the earliest examples of a Roman dialect of sorts; it is in fact one of the very first documenting the evolution of our vernacular.

 

Sources

 

^^1 E. Monaci, A. Pelaez - Storie de Troja et de Roma, altrimenti dette Liber Ystoriarum Romanorum. Testo romanesco del secolo XIII preceduto da un testo latino da cui deriva (Reale Società Romana di Storia Patria, Roma 1920).

^^2 E. Monaci - Sul Liber Ystoriarum Romanorum: prime ricerche (Reale Società Romana di Storia Patria, Roma 1889).

May be worth pointing out that anything you do know will have some serious gaps in it. De Re Militari was pretty available. De architectura less so.