How many vowels and consonants does Standard American English have? 

Your native informant speaks so-called General American or Midlands dialect, and clearly demonstrates what Wm Labov refers to as peripheral and non-peripheral vowel tracks. For example, his “tense monophthongs” /i/ and /u/ clearly begin with non-peripheral “lax” nuclei [ɪ] and [ʊ] and offglide to peripheral “tense [i] and [u], as [ɪ→i] [ʊ→uᵂ]. And his “lax vowels” /ɪ ʊ/ clearly begin with non-peripheral nuclei but also centering offglides to /ə/, as [ɪ→ə] and [ʊ→ə]. I believe that such active gliding gestures (rising or lowering; fronting , backing, or centering) are essential to American English phonology and to sounding American. Even the so-called “short” (lax) vowels exhibit such gestural characteristics. And their absence marks the speech of foreign speakers. For example, the American /æ/ phoneme ranges from extreme high front [i→e] in the Inland North (Chicago), to mid front [e→æ] (NY), to low front [æ→a] (Boston, LA). How is that all Americans understand the entire range of /æ/ without misunderstanding, except that native speakers ignore “place” but and instead attend to the “front opening gesture”? Because although the various phonetic realizations do not even overlap in “place,” all are perceived as segments of the “front-opening continuum.” Likewise the concept of a “back opening gesture” phoneme, unifies the many phonetic realizations of the AW.