Fun fact that's the point, so we can "justify" artistic license for some things :D

Historic knowledge: There was none of the tree. People only started counting years relative to Christ's birth at about 300 A.D.

So... Year 2021 A.D. is actually year 2020. You could say that this year indexing scheme is 1-based. Btw, I'm sure you meant to say 0 C.E. \s

Yes but actually no. Calendars are horribly complicated. IIRC Christ's birth year is about 6 years off. This because the year as we know it was fixated around 300 years Christ's death and by then nobody had (or really cared about) the exact offset.