Hello StudentM,
No, your sentences aren't right. The verb join, very useful in English, has a lot of translations in Spanish depending on the context. And sometimes it doesn't have a specific translation so other verbs are used.
Your sentences should be said as follows:
"Ellos arman el carro". "armar" is used when you put a lot of things together.
The normal way to say the second sentence is "ella empieza la clase en el otoño" or "ella empieza a estudiar en el otoño".
This sentence is one of those that was telling you about where you use a different verb.
You could say "ella SE une a la clase en el otoño", meaning the class already started but she's going to join late"
This is said mostly when you are going to joing a group of people that do something together: "Ella se une (or se va a unir) a.. (las Damas de la Caridad).. en el otoño".
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