TNI is the sum of all "sum of all wages, rent, interest, and profits." Wages are in GDP because the purchase and sale of labour is a transaction. Even in the expenditure approach, G includes government employees' wages.
Did you click the CFI link? The "What is the GDP Formula?" section is less than 200 words.
> dollars spent on imports do not increase local GDP
No. Hence the NX/NFI border adjustment. (In the income approach we count foreigners' domestic incomes and citizens' foreign incomes instead of exports and imports.)
And dollars spent on imports do not increase local GDP