I understand the A.D system was first invented at some point in the late 6th C.
What was used for year-counting before this was created / became widespread - was it simply the consular year naming system?
What system of counting hours were used? How were seasons divided and what were they called?
What calendar was used, the Julian calendar?
How was time calculated, or reckoned - what objects were used if any - for both niche and everyday usage?
I wrote about the Byzantine calendar in a previous answer - Did the Eastern Roman Empire date by Anno Domini or by Ab Urbe Condita?. They used the Julian calendar, but they never switched to the Anno Domini system used in Latin Europe. Instead they used the Anno Mundi, a calculation of the date of creation in the Bible, which was dated specifically to September 1, 5509 BC (when converted to a BC/AD calendar). More can be said about this, especially for the rest of your questions, but that's the answer for year-counting, at least.