Testing a Standardized Approach to Surgery and Chemotherapy for Type I Pleuropulmonary Blastoma or the Addition of an Anti-cancer Drug, Topotecan, to the Usual Treatment for Types II and III Pleuropulmonary Blastoma

Inclusion Criteria: * 21 years of age or younger * Newly diagnosed PPB. Note that patients with known germline DICER1 variant or mosaicism with a large, solid unresectable thoracic mass with imaging features characteristic for Type II or III PPB are eligible without histologic confirmation of the diagnosis if a biopsy of the mass is not considered safe or feasible * Individuals are eligible based on institutional diagnosis of Type I, Ir, II or III PPB diagnosed within 60 days prior to enrollment. Children with Type II or III PPB at risk for clinical decompensation may receive protocol therapy while awaiting rapid central pathology review. Children with Type I or Ir PPB will be assigned to chemotherapy vs. observation based on imaging and central pathology review diagnosis. Type I and Ir patients should not begin chemotherapy prior to return of central pathology results * For patients with Type II or III PPB (within 7 days prior to enrollment): A serum creatinine based on age/sex as follows: * Age: 1 month to \< 6 months - Maximum Serum Creatinine (mg/dL): 0.4 (Male), 0.4 (Female) * Age: 6 months to \< 1 year - Maximum Serum Creatinine (mg/dL): 0.5 (Male), 0.5 (Female) * Age: 1 to \< 2 years - Maximum Serum Creatinine (mg/dL): 0.6 (Male), 0.6 (Female) * Age: 2 to \< 6 years - Maximum Serum Creatinine (mg/dL): 0.8 (Male), 0.8 (Female) * Age: 6 to \< 10 years - Maximum Serum Creatinine (mg/dL): 1 (Male), 1 (Female) * Age: 10 to \< 13 years - Maximum Serum Creatinine (mg/dL): 1.2 (Male), 1.2 (Female) * Age: 13 to \< 16 years - Maximum Serum Creatinine (mg/dL): 1.5 (Male), 1.4 (Female) * Age: ≥ 16 years - Maximum Serum Creatinine (mg/dL): 1.7 (Male), 1.4 (Female) OR - A 24 hour urine creatinine clearance ≥ 60 mL/min/1.73 m\^2 OR - A glomerular filtration rate (GFR) ≥ 60 mL/min/1.73 m\^2. GFR must be performed using direct measurement with a nuclear blood sampling method OR direct small molecule clearance method (iothalamate or other molecule per institutional standard) * Note: Estimated GFR (eGFR) from serum creatinine, cystatin C or other estimates are not acceptable for determining eligibility * For patients with Type II or III PPB (within 7 days prior to enrollment): Total bilirubin ≤ 1.5 x upper limit of normal (ULN) for age * For patients with Type II or III PPB (within 7 days prior to enrollment): Serum glutamate pyruvate transaminase (SGPT) (alanine aminotransferase \[ALT\]) ≤ 135 U/L * Note: For the purpose of this study, the ULN for SGPT (ALT) has been set to the value of 45 U/L * Shortening fraction of ≥ 27% by echocardiogram, or ejection fraction of ≥ 50% by radionuclide angiogram (within 21 days prior to start of protocol therapy) * HIV-infected patients on effective anti-retroviral therapy with undetectable viral load within 6 months are eligible as long as they are NOT receiving anti-retroviral agents that are strong inhibitors or inducers of CYP3A4 Exclusion Criteria: * Administration of prior PPB-directed chemotherapy is an exclusion criterion. Prior treatment for another malignancy is not an exclusion criterion * Patients with known Charcot-Marie-Tooth disease * Female patients who are pregnant since fetal toxicities and teratogenic effects have been noted for several of the study drugs. A pregnancy test is required for female patients of childbearing potential * Lactating females who plan to breastfeed their infants * Sexually active patients of reproductive potential who have not agreed to use an effective contraceptive method for the duration of their study participation * All patients and/or their parents or legal guardians must sign a written informed consent * All institutional, Food and Drug Administration (FDA), and National Cancer Institute (NCI) requirements for human studies must be met