Because in Det er mit mørkeblå æg you have the mit, the adjective takes the e-form which is simply "blå" (like it would after det), however, here it's et lysebåt æg and so the adjective takes the gender of the noun.
Adjectives always take the e-form either when it's describing a plural noun, has the definite article (den/det/de) or a possessive pronoun (Min/mit/mine/din...etc)
They may at one time have been synonyms, but a "bright" color is not just a light color but also a strong, rich color. It doesn't have to be neon, but it is never a pale color.
A light color is neither dark, nor swarthy, nor intense. It is a soft or pale color rather than a bright or rich color. (A secondary meaning is a medium saturation if high in lightness.) Pastels are light colors.
Since we have two words for colors that are not dark, they have diverged in meaning. They are only synonyms when not talking about colors, as in a "light" or "bright" room which is one that is well-lit through good lighting or big windows. Scroll past the noun definitions to get to the adjective definitions. http://www.merriam-webster.com/dictionary/light
Here you will see in the noun section "a bright light" which is different from "a soft light". I wonder if the difference started there. In the adjective section for colors, it is listed as meaning pale. http://dictionary.cambridge.org/dictionary/english/light
Light and bright are not synonyms. Bright has to do with the intensity of the color or its saturation and vividness. Light has to do with the amount of white in it. A more accurate synonym would be PALE, not bright. This is why the pink strawberry in the last exercise does not work well at all.