“Does he have to list her income on his US tax forms?...if so, which form would he use?”====It depends; as long as they file their US returns(fed and sate returns) jointly, they need to report all of their taxable US source and world wide income(including earned income that they earned in Germany);however, if he files his US returns under MFS status(since his Grerman spouse doesn't have any U.S. income, she is not required to pay taxes on her German income to the IRS. In such case, he can choose the marriage filing separately for his own tax return), then, he needs to report only his taxable earned income/unearned income that he earns in Germany(after he claims FEIE if he qualifies it) to the IRS/state.SO, he needs to weigh his options whether he chooses to file one joint return (MFJ), he wants to file separate returns (MFS) .If he and his spouse decide to file jointly, they have to declare their worldwide income (including exemptions, deductions and credits) as a couple in their U.S. return. Joint filing assumes them elect to be taxed on all their worldwide income and supply all pertinent and necessary documentation of tax liability. He may choose the marriage filing separately option if his foreign spouse does not choose to be taxed on her foreign income.Filing separately has higher tax rates and fewer benefits (they won't be able to claim the elderly and disabled tax credit, child and dependent care tax credit and earned income tax credit, among other deductions and credits). Yet, filing separately generally releases you from the burden of any issues or lies made by your spouse in their own tax return.
“I understand that because she is not a US citizen and none of her income is from any US source, Uncle Sam cannot tax it. Is that correct?”=======As mentioned above, it depends.