How to make frosting very white, fluffy, and shiny?
Here are some suggestions:


To make the frosting whiter:


If you use butter, eliminate it. Use all of the other standard ingredients but substitute heavy whipping cream for the butter. Add until you have the consistency you want.
While I can't say I would do this, a viable option would be to substitute a good brand of vegetable shortening for the butter.
Rather than pure vanilla you may consider imitation clear vanilla.
Try adding white food coloring. Regarding food coloring I would recommend a good gel or soft gel/paste formula.

To make the frosting shinier:


If you use butter in your frosting you can try adding more butter.
While I have never cooked cream cheese frosting, there are recipes available online that use corn syrup or glucose syrup and are supposed to produce excellent results in regard to gloss.
After you finish frosting your cake, take a butter knife (non-serrated) or metal frosting spatula and dip in hot water and dry. Go over the frosting again dipping the knife as needed. This should melt the very outside of the frosting only creating the gloss you want.