Most of the planets spin in one direction. The exceptions are Venus (which spins backwards) and Uranus (which spins sideways).
However, planets spinning isn’t what causes the seasons. Earth’s seasons are caused by the tilt of our spin axis. Because the angle that the sun hits the surface changes through the year, it causes temperatures to rise and fall, which is what causes seasons.
So other planets do have seasons. Mars’ axis is slightly more tilted so it has even stronger seasons than us. Saturn and neptune have similar tilts.
Seasons will always go in the same order – warm cool cold cool, but they might well happen at different points (our summer is not at the same time as Mars’).
Almost all of them do, but some don’t. Venus goes backwards (but very slowly, the day on Venus is longer than the year!) and Uranus’ axis of rotation is almost tilted towards the sun so the sun moves in a circle in the Uranian (?) sky.
The reason most planets spin in one direction is that it was the original direction the gas and dust around the sun was spinning, so to conserve momentum (angular) they keep going that way around (just faster). Something funny has happened to Venus and Uranus, however.
Mostly they spin in the same direction, and that is a relic of the direction that the cloud of dust and gas was spinning when the solar system was first formed.
But Venus and Uranus spin the other way, probably because of irregularities in that original cloud of gas.
Any planet with a tilted axis will have seasons, because at different parts of the year, bits of the planet will be closer or further away from the sun. The length and intensity of the seasons depends on how tilted the axis, so Mars has stronger seasons than us because it’s more tilted.