Scientifically, is there such a thing as a coincidence?

Sure, down to some level of temporal precision. Events are co-incident when they occur at the same time. That's it. You stand up to hop aboard the bus when it stops at your bus stop. Standing up and stopping are two coincident events within the ability to measure the time; e.g., your Rolex.

If you used a high precision atomic clock to do the measure, those two events most likely would be shown to not be coincident; one happened before the other for example. But as far as your Oyster Rolex can measure, the two events were coincidental.

So when coincidental means "2.happening or existing at the same time." that happens all the time in day to day life.

If you are asking about it as "1.resulting from a coincidence; done or happening by chance." there are all kinds of event that can only be described through probability.

So even if there is some sort of underlying cause, we cannot describe it with repeatable precision. Rolling a point in craps, for example, results in outcomes that we can only describe through probability; the outcomes are purely chance, random...assuming the dice are fair of course.

Of course. Just because two events occur at the same time or in close proximity to one another does not mean they are causally related. Such an assumption is a common logical fallacy, known as the "post hoc ergo propter hoc" fallacy."

Yes. There is. If I wear the same thing as my friend one day, it's just a crazy coincidence. What that means is that probability just happened to be we wore the same thing, so we call it that.