Players wear helmets and pads for protection. (direct objects, predicate nouns)
Helmets and pads for protection.(direct object)
However, injuries can sometimes be serious or lasting. (indirect objects, predicate
adjectives)
Sometimes be serious or lasting.(predicate adjective)
Drills give the offense and the defense experience. (indirect objects, predicate nouns)
The offense and the defense experience.(Predicate Noun)
http://www.myenglishpages.com/site_php_files/grammar-lesson-direct-indirect-object.php
You are correct, helmets and pads is a noun phrase, the direct object. "for protection" is a prepositional phrase, not part of the noun/direct object It modifies the verb "wear".
There is no indirect object in the second sentence. "serious and lasting" is the predicate adjective phrase.
Experience is the direct object of the verb give. "the offense and the defense" are indirect objects telling to whom the experience is given.
Read about indirect and direct objects in the link above.
To identify the direct objects in a sentence, you need to look for the nouns or pronouns that receive the action of the verb directly. In the sentence "Players wear helmets and pads for protection," the verb is "wear" and the direct objects are "helmets" and "pads" because they are the items being worn.
To find the indirect objects in a sentence, you should look for the nouns or pronouns that receive the action indirectly, usually preceded by the prepositions "to" or "for." In the sentence "However, injuries can sometimes be serious or lasting," there is no indirect object.
To identify the predicate nouns in a sentence, you need to look for the nouns or pronouns that come after a linking verb and rename the subject. In the sentence "Drills give the offense and the defense experience," the linking verb is "give" and the predicate nouns are "offense" and "defense" because they rename the subject "drills."
Lastly, to find the predicate adjectives in a sentence, you should look for the adjectives that come after a linking verb and describe the subject. In the sentence "However, injuries can sometimes be serious or lasting," the linking verb is "be" and the predicate adjectives are "serious" and "lasting" because they describe the subject "injuries."