Whisk palm sugar and 1 tbsp water in a medium bowl to dissolve sugar. Whisk in chiles, garlic, lime juice, and fish sauce; season with salt. Balance with more sugar, lime juice, or fish sauce if needed.
Toast coconut in a dry small saucepan over medium-high heat, stirring occasionally, until golden brown, about 4 minutes. Transfer to a small bowl.
Heat oil in same saucepan. Add half of shallots and fry, swirling, until golden brown and crisp, about 3 minutes. Transfer to paper towels with a slotted spoon to drain; season with salt.
Cook peanuts in shallot oil until golden brown, about 2 minutes. Transfer to paper towels to drain; season with salt.
Remove peel and white pith from pomelos. Tear membrane off and pull segments into large pieces, transferring to a large bowl as you go. Add cilantro, remaining shallots, and half of dressing and toss to coat. Add coconut, peanuts, and dried shrimp; toss again. Divide among plates, drizzle with remaining dressing, and top with fried shallots.