Does this sentence have correct parallel structure: Clara not only wants money but also wants fame.
Yes
What is an independent clause?
A complete sentence. It has a subject and predicate.
Is this sentence parallel: Languages consist of read, write, speaking, and listen in our daily life.
No.
Parallel: Languages consist of reading, writing, speaking, and listening in our daily life.
A dependent clause does not...
Make sense on its own
Write this sentence so that it is parallel: Mary likes hiking, swimming, and to ride her bicycle.
Mary likes hiking, swimming, and riding a bicycle.
Fix this sentence so that it is parallel: The coach told the players that they should get a lot of sleep, that they should not eat too much, and do some warm-up exercises before the game.
The coach told the players that they should get a lot of sleep, that they should not each too much, and that they should do some warm-up exercises before the game.
Fix this sentence so that it is parallel: The author's main pieces of evidence are her feelings, experiences from her childhood, and implies the effect these experiences had on her.
The author's main pieces of evidence are her feelings, experiences from her childhood, and the effect these experiences had on her.