In manuscripts of Classical works, capital letters (so Δ instead of δ) are used frequently, yet when modern publishers publish these works, they use lower case letters. Then there all the rules of breathings and accents over the letters which can't have been invented by Alexandrian scholars. When were Greek lower case letters used first, and when did they become common?
The Greek lowercase forms (aka miniscule as opposed to majuscule) became common starting during the 9th and 10th centuries. It was fairly widespread by this time. Modern Greek writing developed from these forms a bit later when printing became more widespread, and it's been that way since.
edit: /u/talondearg beat me to it. I should refresh more often.
Lower case writing (miniscules) appear and become prevalent from around the 9th and 10th century CE onwards, primarily in Byzantium, but spreading elsewhere. Miniscule type manuscripts later become the standard for the latter medieval period, and thus the basis of print editions post-Renaissance when the invention of the printing press made such things possible.
Accents are accredited to Aristophanes of Byzantium, ca. 257 - 180 BCE, but took some time to spread. I don't know why you think they "can't have been invented by Alexandrian scholars", this is not generally in doubt. However it took considerable time for them to start appearing widely in writing.
I can't confirm from sources at hand when breathing marks in particular came into common usage.