The details and current status of data requests submitted through the Data Request Help Desk page can be seen here.
Number of people who have applied for coming to the US from different countries, how many were given visas, what types of visas were given (tourist, student, business, PR, etc.), eventual states they settled in, religion of people who applied.
dhs open data poc has been notified of user data request.
Most of these data actually belong to the State Department, not DHS.
DHS would have info on immigrant admissions and (initial) states of settlement. Data on permanent residents are available here (https://www.dhs.gov/immigration-statistics/lawful-permanent-residents), and data on temporary residents available here (https://www.dhs.gov/immigration-statistics/nonimmigrant).