Is it permissible to treat disbelieving nations in kind by imposing a tax on their goods, following the example of Umar ibn al-Khattab, may Allah be pleased with him, or is that considered an unlawful tax (maks)? And what is the ruling if the state imposing the taxes is Muslim?

There is no harm in imposing taxes on the goods of non-Muslims, especially if it is a reciprocal measure. Umar ibn al-Khattab imposed taxes on the goods of non-Muslims as a reciprocal measure for what they took from Muslim traders, and this is called "al-ta'sheer" (the levying of a tithe). As for the goods of Muslims, it is not permissible to impose a tax on them except in exchange for real services; otherwise, it would be considered an unlawful maks (illegal tax), with the exception of the obligatory zakat (definition).