Mature-vs-precursor first.
The decisive split in B-cell neoplasms is whether the cell is a precursor (immature) or a mature B-cell. Three markers settle it here:
• $TdT$ negative
• $CD34$ negative
• surface $Ig$ POSITIVE
This triad is definitively mature B-cell. That single deduction eliminates B-ALL, because B-ALL is a precursor tumour that is TdT+, CD34+ and surface-Ig-.
Now place the mature B-cell tumour.
Remaining mature B markers: $CD19+$ (B lineage) and $CD10+$ (germinal-centre origin). A germinal-centre, CD10+ mature B-cell, high-grade lymphoma in a 10-year-old boy with a fast-growing cervical node, and a smear showing a starry-sky pattern of medium-sized cells with deep-blue vacuolated cytoplasm, is the textbook picture of Burkitt lymphoma.
Clearing the remaining distractors.
DLBCL - mature B too, but an older-age, non-classic-childhood entity and not the canonical CD10+ starry-sky tumour intended here.
Anaplastic (ALCL) - a CD30+/ALK+ T or null-cell lymphoma; it would NOT be CD19/CD10/sIg positive.
Conclusion: mature germinal-centre B phenotype + child + starry-sky morphology → Burkitt lymphoma, Option A.