1) I placed Jesus's birth in 2 BC based on revised chronology, details are available at dec25th.info Jesus's birth was indeed on December 25th, but in 2 BC, not in AD 1; our calendar is slightly shifted due to miscalculations in the Middle Ages. Also, this matches perfectly with Jesus's age reported in Luke 3:23, being 30 years old when He began His ministry, which is commonly dated in AD 28-29.

2) Artaxerxes's concessions to Ezra might have been in 457 or 458 BC, the dating isn't known with precision. I put ~455 BC to have an exact 490 years match with AD 35 (a very solid estimation for the date of Philip's ministry in Samaria, the first time the Gospel was preached to non-Israelites), however if it turned out to be not exactly 490 years, this shouldn't be an issue: the match is still very close.

3) Jesus's baptism and beginning of ministry likely occurred in late AD 28 or early AD 29; making Jesus 30 years old, since He was born in December of 2 BC. I put AD 28 for clarity and making the 30 year match exact, but it might have been AD 29.

4) Technically, Nero was the fifth emperor of Rome, not the sixth, because modern historiography considers Augustus to be the first emperor, not Caesar; however, Caesar ruled the whole Roman world, concentrated all powers in his hands, ended the Roman Republic and was deified after his death; moreover, the Roman emperors were not officially "kings" anyway. So in biblical eschatological terms, I think it's safe to assume that Julius Caesar is the first "king", not Augustus: therefore Nero is the sixth king, rising after five are fallen. Nero is also commonly referred to as the "sixth Caesar".