No. You have to be a natural born citizen to be eligible for the Presidency. That includes those born in the US. Also, current U.S. statutes define various categories of individuals born overseas as...
You must be a "natural-born citizen, NOT "native-born". Current U.S. statutes define various categories of individuals born overseas as citizens at birth i.e. natural born, including (for example)...
There is no such requirement - indeed, the only job which is restricted to people who are born in the US is that of President of the US. Any other job is open to anyone who was born anywhere.