These are some of the greatest questions to ask! In my opinion, time is a dimension too. I work in medical physics and we routinely use time as a dimension whether as an axis on a plot or an experimental variable.
What's more, time is relative. The passage of time as we think of it is a human construct that only really makes sense on this planet and under typical conditions. When things speed up enough for relativistic effects to occur, things get weird!
As for when time began? I'd like to think that it was before the big bang. If an incredible amount of energy created all the matter that we see today, that energy had to come from somewhere and that somewhere must have existed before the big bang. And therefore that somewhere had age in the same sense that we think about aging now... Therefore time...
What just happened? I blacked out there for a second! Great post... I think?
I am so happy right now. Thank you for the beautiful insight. And yes great post. Also like you said we understand time under our typical conditions.. I want to know what happens when those conditions are change. Thank you again