The son of a black and white couple is (often) considered black. This is because when there was slavery, the white owners would often rape the black slaves and the kids would be slaves. So the "black" population ended up with a mixture of white and black genes which varied by person, and to qualify as "white" you had to be 100% white. This meant that even after slavery, the mixed population had to deal with the same discrimination as "pure" blacks, and so they formed a single ethnic group.

There is a long history of terms for black people going out of style and being replaced by new ones. It's called the "euphemism treadmill" - once racists started using a term as a slur, tolerant people looked for a new term.

Latino is anyone with ancestry in Latin America. A lot of people in the US treat it as a separate race. But the US census treats it separately from race, i.e. you can be a Latino white, a Latino black, and so on. I would say the racism issue with Latinos in the US is similar to Poles in the UK, they are an immigrant group from poorer countries which is seen as taking jobs and bringing crime.

"Italians are not white" is a thing a few weirdos say online, it's not something you are likely to hear from a "normal" racist in day to day life. (Note: 100 years ago it was common to say that "Italians are not white", at that point Italians were a poor immigrant group, similar to Mexicans today.)