Are all planets in our Solar System in the same plane ?
All the planets except for Pluto are in approximately the same plane, but the plane of the orbit of Pluto is inclined by about 17o relative to the plane of the other planets' orbits.
Perhaps that is another reason (besides size) why Pluto was properly demoted to a dwarf planet.
While all the major planets are close the same plane, it's not exact.
Mercury and Venus can be as much as 3 degrees out at times.
These faster moving planets make their closest approach to Earth at least once every Earth year, at which point they are positioned between the Earth and Sun.
However it is only occasionally that the alignment is such that we observe the planet crossing the face of the Sun.
Planets are the coalesced remains of the accretion disc that encircled the sun during its birth. The rings of Saturn are analogous, The particles that comprise the rings all orbit very nearly in the exact same plane. Picture these particles clumping together to form moons. They too would orbit in the same plane. It is certainly possible these moons, over time, could be perturbed out of their orbital planes by their sibling moons, other planets or the occasional rogue wanderer. The early solar system was a pretty chaotic environment. Aspiring planets collided. Some may have acquired more elliptical orbits dragging one another off course as they approached and receded from the sun. By the time all the planet orbits stabilized, its no surprise they have drifted away from their original orbital planes.
Less than once per year for Venus: Both Earth and Venus orbit in the same direction, so Venus always has to "catch up". The closest approach happens every 584 days (+- a few days). For Mercury it happens every 116 days on average.
I think these images might be the best way to visualize the answer
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