Do establishments on native American land charge US state and federal taxes on normal goods and services?

Answer 1

complicated.
Federal Reservations are those recognized essentially as foreign governments by the US and have formal treaties. Taxes are not charged for State or Federal purpose, and bear some similarities to federal zones like D.C. or Puerto Rico. State Reservations are those tribes with sufficient power to force state recognition and are not federally recognized and will be subject to federal taxes, but (usually, depending on the nature of the compact with the particular state) not by the state. Other tribes with "reservations" are not recognized and fully subject to taxes.
HOWEVER, the issue is further complicated by where the goods aand services are produced, offered and sent and by whether or nnot the firm is a business established and licensed by that tribe, whether that business has it's headquarters on the reservation, the type of business (corporation, llc, partnership, sole proprietor, etc...) and where the owners / agents for services of the business live.
sorry. can't be more specific without knowing which tribe, which state and other details mentioned above.
keep in mind excise taxes, tariffs, and other types of indirect taxes and goods that may occur when crossing a border from native lands into U.S. or American States territories.

Answer 2

many have revenue agreements in place with various governmental agencies, but it's not the same as off-rez businesses.

Answer 3

NO.