I ate the apple - is a sentence. Even I have eaten is a sentence because it is a complete statement although it does not specify what I have eaten. A subject is something that a verb needs. Verbs which take direct objects are known as transitive verbs. Indirect objects do not answer straight questions, but indirect ones.
Agents apppear with passive voices of verbs.
Transitive verbs always have a direct object. But some verbs can be transitive and intransitive. Eat is one of these. The first time it is transitive. The second time it is intransitive.