Must alkali make purple litmus test solution turn blue, colorless phenolphthalein test solution turn red Alkali can make purple litmus test solution blue, colorless phenolphthalein test solution red

Must alkali make purple litmus test solution turn blue, colorless phenolphthalein test solution turn red Alkali can make purple litmus test solution blue, colorless phenolphthalein test solution red

This sentence is wrong, should say: not necessarily!
For example, when sodium hydroxide is dissolved in water, the solution can make the phenolphthalein test solution turn red, because sodium hydroxide is dissolved in water and can ionize OH- radical ions. When the alkali is insoluble in water, it can not change the color of phenolphthalein. For example, copper hydroxide can not change the color of phenolphthalein, because it is insoluble in water and can not ionize OH- radical ions, so it has no such property. Therefore, the soluble alkali can change the color of indicator.

What color do litmus and phenolphthalein show when they encounter acid and alkali? Also, what is the reason why acids and alkalis change color?

The litmus turns red with acid and the litmus turns blue with alkali. The phenolphthalein turns red with acid and the phenolphthalein turns red with alkali.