Why do we use right triangles to find the dimensions of other shapes so often (eg. parallelograms and non-right triangles)?
Because of the fixed relationships between sides and angles in a right triangle that allows consistent rules like the Pythagorean theorem and use of trigonometrical functions, we know quite a lot about them if given even a little information; we take advantage of this fact to examine shapes that we know less about on their own.
In a reaction mechanism, why does changing the concentration of a reactant only involved in a "fast" step not effect the overall rate of reaction?
The rates of "fast" and "slow" steps in reaction mechanisms are so many orders of magnitude apart, that the "fast" step can be considered relatively instantaneous. Because of this, any minor alterations to the availability of reactants for that step will not have a meaningful affect on overall speed. It would be like factoring in the effect of a bug hitting the windshield of a car on the highway on its speed.
Why does phenotypic similarity between two species (eg. bio-luminescence) not necessarily indicate that the species have a close taxonomic relationship?
The phenomenon of convergent evolution means that unrelated species can often adapt similar survival traits to fill the same ecological niche. Often times, the process of natural selection leads to two species developing incredibly similar traits through entirely different evolutionary pathways.