Asking for the direction of the field at a particular point is the same as asking for the direction of the force experienced by a positive test charge placed at that point. A test charge is a charge with a magnitude so small that placing it at a point has a negligible affect on the field around the point.
In this regard, are point charges always positive?
Positive charge created a field that pointed radially away from because it always repelled the positive test charge. But a negative charge creates an electric field that points radially into because it's always attracting a positive test charge.
Why do electric field lines come out of positive charges and enter negative charges?
The direction of the electric field is always directed in the direction that a positive test charge would be pushed or pulled if placed in the space surrounding the source charge. As such, the lines are directed away from positively charged source charges and toward negatively charged source charges.