The simple subject is the person or thing talked about in the sentence, without the words that describe or modify it.
The simple predicate is always a verb showing an action or a state of being.
Examples:
In the first sentence, the simple subject is friend. It is the person being talked about, without the words describing him/her.
The simple predicate is will visit. It is the verb showing an action or state of being.
Similarly in the other sentences, brother, I, mother, and daddy are simple subjects. Will bring, will play, will cook, and promised are simple predicates.