Learn Dutch: Hij is tevreden, maar nog afhankelijk. - He is satisfied, but still dependent.

You only need the fixed preposition when you are actually mentioning the object (the thing someone is satisfied with or dependent on). Since this sentence just describes his general state of being, no prepositions are needed.

If I wanted to say what he is satisfied with and dependent on, which prepositions go with these adjectives?

For tevreden (satisfied), you use met or over. For afhankelijk (dependent), the fixed preposition is van. For example: Hij is tevreden met zijn baan, maar afhankelijk van zijn ouders (He is satisfied with his job, but dependent on his parents).

I usually use nog steeds for "still." Why is it just nog here?

Both nog and nog steeds translate to "still" and can often be used interchangeably. Nog steeds slightly emphasizes that a situation is continuing for a long time, whereas just nog is a shorter, standard way to say it. Either would work perfectly in this sentence.

Why doesn't the second part of the sentence have a subject or verb after maar?

Dutch often drops words to avoid repeating them, just like English does. The full second clause would be maar hij is nog afhankelijk. Since the subject and verb (hij is) are identical to the first half and joined by the coordinating conjunction maar (but), you can naturally leave them out.