Theorem: If two lines intersect, then exactly one plane contains both lines. So, when two or more lines intersect at one point, they lie exactly in the same plane. When two or more lines intersect at one point, their point of intersection satisfies all equations of those lines. In other words, the equations of these lines have the same solution, which is the point of intersection.
If two different lines intersect, they will always intersect at one point.
In Euclidean plane geometry two infinitely long straight lines intersect at only one point
No, two straight lines can intersect at only one point and that is their point of intersection.
Curves yes, straight lines no
Perpendicular lines are lines that always intersect either at just one point, two points or several more.
Perpendicular lines intersect at one point only.