Your economy of expression works to obfuscate your meaning,
but I think you may be referring to a 'parallel' line.
Yes, it is possible.
point, line and plane
A ray
Angles that share a common end point and a common line segment but no common interior point (two angles that are next to each other)
When the line is inclined to the plane. That is, it is not in the plane nor is it parallel to it.
Concurrent or intersecting lines.
Yes, it is possible.
Plane. A point has no dimension, a line has one dimension, and a plane has two dimensions.
point, line and plane
point * * * * * or, nothing (if the line is parallel to the plane).
Angles that share a common end point and a common line segment but no common interior point (two angles that are next to each other)
plane
A ray
Angles that share a common end point and a common line segment but no common interior point (two angles that are next to each other)
A plane intersects a line at a point, and i plane intersects another plane at a line.
Two straight lines in the same plane can't possibly have more than one point in common, unless they are both the same line. If they're parallel, they have no common points. If they're not parallel, then have exactly one common point. If they're the same line, then every point on one line is also on the other one.
When the line is inclined to the plane. That is, it is not in the plane nor is it parallel to it.