None of these questions matter. No passing in intersections.
It's likely the lanes leading to intersection had solid lines (indicating no passing) but cyclists are often allowed to pass when cars are not.
Passing in intersections is more risky.
Anyway, the original question was if the passing cyclist had a "right" to pass.
The answer to that is clearly "no". No one has a "right" to pass and the passing vehicle doesn't have the "right of way" either.
You may only pass when it's safe to do so.
And, as many people have said, the OP chose a poor lane position and didn't signal.
The passing cyclist was putting too much trust in knowing what the cyclist in the intersection would do.
The reasons a careful driver wouldn't pass in this situation apply to cyclists (even if cyclists have somewhat more latitude).
In any case, given that the OP has no way of keeping others from passing him, it's really on him to take care (which he appeared to do).