Cengiz ,
In the first sentence, it's nominative case, masculine, singular. It means that "there is experience" you can check yourself and say: У етого автора большой опыт - У этого автора ЕСТЬ большой опыт". The second sentence is genitive, masculine and singular. In Russian we almost never put the verb "to be" in the sentence like this.
The third sentence is a feminine noun in the genitive case. It's correct and the ending must be "и".
The fourth sentence is like this because of the verb вижу. The particle "не" works as a negation. Without не it would be "Я вижу нашего ученика". Itäs masculine, genitive.