I would be using your question and your points in my answer.
"On a generation starship headed to a nearby planet, what would be the most beneficial survival courses to take?"
Then you pointed these out
1)The planet the colony will be set on is extremely earthlike. Same amount of gravity, oxygen to breathe, and liquid/frozen water. It even has some life and it’s mostly non-hostile.
2)The people take these lessons as soon as they get on the ship, and when their kids turn 4 they go to school and are also taught.
3)The leaders want everyone to know the most useful survival skills.
Which leads me to think that you want your "colonizers" to survive on a new planet.
These are the things which I have in mind.
1) Military exercises - The soonest that you dock your ship on something which you do not know what lies in it, you have to be prepared. you crew must all be equipped with the best weapons which they can use, and the best armors they could wear. To use them efficiently, your leader must train every crew member of any ship with the best military training ever to fully utilize their gears.
2) Life Sciences - (Anatomy, Chemistry, Biology.. etc.) Your crew is in a planet which they literally have no idea about the vegetation around them. They must learn how to classify if a plant or animal is edible or not, specially the crew who would be the "Pioneers" of the planet. Your crew must also classify if the planet is rich in usable materials and such.
I think these are the key factors which you need to have in order to survive on a new planet, my answer might be too broad for you, but you have to consider the fact that you have no idea about the planet, and your leader wants to colonize it. Your pioneers must survive their first days, and as you have pointed out, they came on spaceships, not on boats or any other primitive transport. So I think with these skills, your crew would survive from day one until they have conquered the planet.