Peace - "Peace" is the Greek term that means harmony between individuals and nations" and the general idea of safety, security, and prosperity. It is the opposite of the state of war. In Hebrew, the word for peace was used in salutations and as an inquiry as to one's health.

be -- There is no verb "be" here in the Greek source but it is implied by the noun in the form of a subject having no verb associated with it.

with -- This word "with" comes from the dative case of the following word that requires the addition of a preposition in English. The most common is a "to" for the English indirect object. However, the translator can choose other prepositions: "with,"  "in,"   "of,"  "as," "by," "for," "at," or "on" depending on the context.

you.  -- The Greek pronoun "you" here is plural and in the form of an indirect object, "to you," "for you," etc.

As -- "As" is from a Greek word that means which means "even as," "how," and, in relating to time, "as" and "when."

the -- The word translated as "my" is the Greek definite article. When not preceding a noun, takes the meaning of "the one" or, in the plural, "the ones." The Greek article is much closer to our demonstrative pronouns ("this," "that," "these," "those") than the English "the." See this article for more. 

Father -- "Father" is the Greek noun that means "father" or any male ancestor so "forefathers." It is the word that Christ uses to address his own Father.

has -- This helping verb "has " indicates that the verb is the tense indicating an action completed in the past.

sent--- (CW) The "sent" here is a word that means "to send off" and "dispatch." It is the source of our word "apostle." This word is not the simple "send" but a more complex one that means "send out" or "send from." The common word for send is different, appearing below.

me, -- "Me" is the regular first-person pronoun in Greek as the object of the verb or preposition. As the object of a preposition, an accusative object indicates movement towards something or a position reached as a result of that movement.

missing "also"  -- (MW) The untranslated word  - This is from "also...I," a contraction of the conjunction "and" and the first person pronoun, "I/me."  The "I" is the subject. It appears below.

I -- This "I" is a subject from the contraction above. When the subject of the sentence is part of the verb, this pronoun's accentuates who is speaking "I." Saying "I myself" captures this feeling in English.

missing "myself" -- (MW)  The subject pronoun repeats the information in the verb so it should be repeated in English like "I myself."

am -- This helping verb indicates the present tense of the verb. It is used here to form the present, progressive tense, which doesn't exist in Greek but which can smooth the flow of English sentences.

sending -- "Sending" is from a Greek verb that means "send," "send forth," "send away," "conduct," and "escort." This is the second most common word Jesus uses that is translated as "send out," but this one doesn't have the prefix that has the sense of "out." This is the simple word for send, different than the one above.

you. -- The "you" here is the second-person, plural pronoun in the form of an object of the action or preposition.