A group of words in the form of a question should be turned around and made into a statement to easily find the sentence parts: "He has made another serious mistake." "Babies do eat soft food why."
Find the verb first, then see if there is a helping verb in front of it. To find the object, put the subject and verb together and ask what. If there is a "what" word, it is a direct object (if following an action verb).
#1: made is the verb; has is a helper, so the simple predicate is has made. Ask who has made? The answer is "he". He is the simple subject. He has made what? mistake. Mistake follows an action verb so it is a direct object. The words "a" and "serious" modify or describe the mistake.
#2: eat is the verb and do is its helper. What do(es) eat? babies. Babies do eat what? food, which is a direct object. Soft is a modifier of the noun "food".
In complete subjects and predicates, the complete predicate usually begins with the verb, unless the verb has a helper (which both of your sentences do have). The predicate and its objects, including modifiers, are the complete predicate. All of the remaining words are the complete subject.
"He has made another serious mistake." He is the complete subject; the remaining words are the complete predicate.
"Babies do eat soft food why?" Babies is the complete subject; the remaining words are the complete predicate.
Both sentences are written in standard English Interrogative form with split Modal Verb phrase. In the first sentence the modal verb phrase "has made" is split by the Subject "he." In the second, the Modal Verb phrase "do eat" is split by the Subject "babies." These follow the standard interrogative syntactical form of Modal Subject Verb Object. In the second sentence, the modal "do" is preceded by the Interrogative "why" adverb, thus creating an interrogative wh-clause.
In both sentences, the Noun Phrases that follow the Verbs fill the Object slots and are both Direct Objects (indirect objects answering "whom?" would precede direct objects but in both cases are not part of the sentences). A noun phrase comprises a group of words that may be determiners and modifiers preceding a head noun. In the first sentence the Noun Phrase "another serious error" is a noun phrase comprising a Modifier adjectival qualifier ("another"), a Modifier adjective ("serious"), and the Head Noun ("error") of the Noun Phrase. In the second, the Noun Phrase "soft food" comprises a Modifier adjective ("soft") and the Head Noun ("food") of the Noun Phrase.