Are the following sentences correct?

"How many emigrated to the United States?"
"What was a reason for immigration?"

Yes.

https://public.wsu.edu/~brians/errors/emigrate.html

The first sentence, "How many emigrated to the United States?" is grammatically correct, but it lacks context. To answer this question, you would need to find and refer to a reliable source such as a census report, government statistics, or historical records. These sources can provide the exact number of people who emigrated to the United States during a specific time period.

The second sentence, "What was a reason for immigration?" is grammatically incorrect. It should be "What were the reasons for immigration?" To find the reasons for immigration, you can consult various sources such as historical records, academic research, or demographic studies. There are several factors that typically contribute to immigration, including economic opportunities, political instability, social unrest, war, and religious persecution. By examining these sources, you can gain a comprehensive understanding of the reasons people choose to immigrate to a particular country.