Cisplatin and Combination Chemotherapy in Treating Children and Young Adults With Hepatoblastoma or Liver Cancer After Surgery

Inclusion Criteria: * Patients in Group F must have a body surface area (BSA) \>= 0.6 m\^2 * Patients must have a performance status corresponding to Eastern Cooperative Oncology Group (ECOG) scores of 0, 1, or 2; use Karnofsky for patients \> 16 years of age and Lansky for patients =\< 16 years of age; patients who are unable to walk because of paralysis, but who are up in a wheelchair, will be considered ambulatory for the purpose of assessing the performance score * Patients must be newly diagnosed with histologically-proven primary pediatric hepatic malignancies including hepatoblastoma or hepatocellular carcinoma, except as noted below; patients with a diagnosis of hepatocellular neoplasm, not otherwise specified, should be classified and treated per hepatoblastoma treatment arms; note that rapid central pathology review is required in some cases; please note: all patients with histology as assessed by the institutional pathologist consistent with pure small cell undifferentiated (SCU) HB will be required to have testing for INI1/SMARCB1 by immunohistochemistry (IHC) according to the practices at the institution * Patients with histology consistent with pure SCU must have positive INI1/SMARCB1 staining * For all Group A patients, WDF status as determined by rapid review will be used to further stratify patients to Group A1 or A2 * For Groups B, C and D, rapid review is required if patients are either \>= 8 years of age or have an alphafetoprotein (AFP) =\< 100 at dia…