He -- (CW) The word translated as "he" is the Greek definite article, without a noun, it has the sense of "the one." The Greek article is much closer to our demonstrative pronouns ("this," "that," "these," "those") than the English "the." See this article for more. This is not the common pronoun "he."

that -- (IW) There is nothing that can be translated as "that" in the Greek source. It was added because the next verb was translated as active rather than as a participle.

believeth -- (WF)  The Greek word translated as "believe" does not apply to religious belief as much as it does trusting in other people, especially their word. Christ usually uses it in contexts, as the one here, that apply to trusting words. The negation of "belief" with the objective, instead of subjective, negative, equates trust with a fact. The form of the word is not an active verb but a participle.

on --  (CW) The word translated as "on" means "into" a place, "towards" as a direction, "in regards to" a subject, and "up to" limits in time and measure. This is not the common word that means "on." This does not likely mean "in me" here, but "as much as."

me, -- "Me" is the regular first-person pronoun in Greek as the object of the verb or preposition.

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 "the" is the Greek definite article, without a noun, it has the sense of "the one." The Greek article is much closer to our demonstrative pronouns ("this," "that," "these," "those") than the English "the." See this article for more. 

scripture -- - (CW) "Scriptures" is a noun that means "writing", "the art of writing," and "that which is written," so, the "writings." It doesn't have the specific sense of religious writing that "scriptures" does. It might also be worth noting that the Greek word translated as "scriptures" literally means "a drawing." For the Greeks, both drawings and words created a "picture" or a man-made, artificial representation of reality.

hath -- (WT) This helping verb "hath" indicates that the verb is the tense indicating an action completed in the past. This is not the tense of the verb here.

said, - The word translated as "speak" means "to say" and "to speak." It is one of the two most common words translated "speak," "say" and "tell," but it has more a sense of addressing and proclaiming.

out of -- The Greek preposition translated as "out of" means "out of" or "from." The word also means "beyond," "on," "in," "since," or "by"based upon its context. However, in Greek, they use the genitive case instead of a preposition for the types of phrases that are translated into English "of" phrases.

his -- The word translated as "his" is the Greek word commonly translated as third-person pronouns in English.  This pronoun follows the noun so "of his."

missing "the"  -- (MW) The untranslated word is the Greek definite article,"the," which usually precedes a noun and, without a noun, takes the meaning of "the one." The Greek article is much closer to our demonstrative pronouns ("this," "that," "these," "those"). See this article for more. 

belly   - "Belly" is from the Greek word meaning any abdomen, referring generally to any opening in the body. In Greek, the home of the most basic emotions, food, sex, and other forms of immediate gratification.  The Greeks considered the belly the source of our animal impulses and desires: food, sex, and other forms of immediate gratification.

shall -- (CW) This helping verb "shall" does not indicate the future tense, but that the verb describes a possibility, the subjunctive voice. A "might" or "should" in English is more appropriate, but is assumed in an "if/when/whoever/except" clause. Helping verbs are not needed in Greek since the main verb carries this information in its form.

flow   -  "Flow" is a verb "to flow", "to stream", "to run", "to fall", and "to be in a state of perpetual flux and change," [of persons].

rivers   - The word translated as "rivers" means a "river," and similar existing bodies of water

of -- This word "of"  comes from the genitive case of the following word that requires the addition of a preposition in English.  The most common is the "of" of possession.

living -- The verb means "live," "to be alive,” “to be full of life," "to be strong," and "to be fresh." So it is life in the sense of having a vital life, strong and growing. Perhaps in English, “thrive” would be more precise.

water. -- "Water" is the noun that means "water," "spring water," "drinking water," "rain water," "rain," "time running out" (from the water clocks used in courts),  "liquid," the constellation Aquarius, the winter solstice, and a place with mineral waters.