Assuming that the flare was fired at t= 0, yes. That's a reasonable assumption but the problem should have said something like "in metres t seconds after firing".

It's easy enough to check: so and . No, that's not the same thing as .B) what height is reached by the flare.

*For this I "completed the square" and got "h=-5(t-4)² + 78"...don't know if that's right of what to do after*

Now you know, I hope, that a square is never negative so is never positive and the height is always less than to equal to its value when t= 4.

In your answer to a, you said that the tower was 10 metres above the ground since h(0)= 10.C) how long is it in the air (until it hits the ground)

I have no idea here

That means you are taking h= 0 at the ground. Solve the equation