Can this Azelaic Acid 10% w/w Cream remove dark spots and pigmentation?

Azelaic acid is actually a reasonably gentle option and is often used for conditions like rosacea or mild acne that show up as redness and small bumps, so it's a fair choice to consider. Since your skin is sensitive, I'd still suggest easing in perhaps every other day at first to see how it responds before using it daily. A dermatologist looking at those bumps directly would help confirm what's actually causing them and whether this cream is the right match.