Well in this country we define citizens as anyone being born as United States citizens as being natural born. They can be from any country and their child may be a citizen of the U.S. This can be controversial but ultimately it does very little for anyone to do this and if so can lead to some conflict on federal or state terms. Besides that you can be a citizen even if you were not born in the US this is either done by immigrating legally and passing various tests or by having one parent be an American citizen. Either or is acceptable.
Burr was a Democratic-Republican. The Democratic-Republicans supported government authority being dispersed among the people at a more local level. Hamilton was a Federalist. Federalists favored a strong, centralized federal government.
A "seniority system" is an employment system that allots to employees rights and benefits according to the length of their employment. The principal feature of all seniority systems is time.