Why is KHP a standard solution? And why is 250ml of 0.01M NaOH not?

Answer 1

KHP is used as a standard because it is easily made completely anhydrous (or very nearly so) without any degradation, and it is stable on standing (reasonable amounts of time).

The reason NaOH is not used as a standard is the "dry" pellets contain a variable (~10-15%) water, and it gradually reacts with CO2 in the air and partially converts to Na2CO3 (even when in solution).

The big deal about anhydrousness is when you are weighing something you want to use as a standard you want to be absolutely certian that all of what you are weighing is active material so your work will be accurate and reproducible.