Here we use the word es that is the conjugation of the verb ser for the third person singular in the simple present. In this sentence, we use the verb ser as occupation. Basically, it's what someone does for a living or as a hobby. So Carlos is not a student. The other items use the verb ser with incorrect conjugations.
Here we use the verb ser as physical descriptions, talking about the essential quality that describes some people as the body frame. Hence somos is the conjugation of the verb ser for the first person plural in the simple present. Therefor, Nosotros somos muy delgados means we are very thin.
Here we use the verb ser as characteristics, that are personality descriptions of a person. This characteristic here is that my children are lazy. Since mis hijos can be replaced by ellos, then we need to use the conjugation of the verb ser that matches the third person plural, which is son. Therefore, my children are lazy.
Here we use the verb ser as occupation again. So here a woman introduces herself as a lawyer. In this way, soy is the conjugation of the verb ser for the first person singular in the simple present. In Spanish, it is common not to include the subject pronoun in sentences. Thus, it is also valid to say soy abogada.
Here we use the verb ser as description, but talking about the essential quality that describes a person that is the nationality. So here we use a negative sentence to say that Clara is not a Cuban. Since Clara can be replaced by ella, we need to use the conjugation of the verb ser that matches the third person singular in the simple present, which is es.
