Where the orbits cross is only part of assessing collision probability. You also have to know the time at which the two spacecraft reach the same point. Unless the crossing happens at the same time both spacecraft are there, no collision can happen.
For example, it is perfectly safe to put multiple satellites in identical orbits, but separated from each other by a small amount of time. This is exactly what is done in many operational constellations, the most extreme of which is StarLink. They have sixty satellites sharing each orbit, but they will never collide because they are spaced equally around the circle and all moving at the same speed.
Similarly, multiple sets of circular orbits can cross each other safely, as long as the satellites in each plane are phased properly. For example, again picking on StarLink, six circles of sixty satellites can all cross at one point and still keep at least 1 degree separation between them, if one circle goes through the crossing at 0, 6, 12... degrees of mean motion, the next at 1, 7, 13..., the next at 2, 8, 14... etc. The standard way to design one of these is the Walker Star constellation.
Different semi-major axis or different eccentricity can each alone cause collision, depending on the time phasing. Both together don't have to cause it, depending on orbit planes and time phasing. Orbits in different planes can and do cross, and have historically caused actual collisions. The trouble with collision avoidance (also called conjunction assessment) is that Kepler's equation, which describes the time behavior, is not analytically solvable for non-circular orbits. Therefore, you can't avoid having to do some numerical solution, and you quickly discover that you can't predict probability of actual collision without a good propagator and a good covariance estimate.