How to pronounce the שְׁוָא ?

The pronunciation of the "pronounced" שְוָא presented in these recordings may sometimes differ somewhat from what is presented in biblical Hebrew textbooks. We only pronounce the שְׁוָא in consonant clusters where the consonants are such that it impossible to pronounce them without inserting a sort /uh/ or /eh/ vowel sound. Compare, for example these two sets:
a) plee
versus b) lpee.
In example b) it is impossible to not say leh-pee
So when there are two consonants that can't be pronounced without inserting that /uh/ vowel, we do. That שְׁוָא is what your book calls a vocal shva Historical Note
There are two kinds of שְׁוָאִים. The שְׁוָא נָח was always a "zero vowel". It's purpose is to mark the end of a syllable.
family מִשְׁפָּחָה = mish-pa-xa
The שְׁוָא נָע (mobile or vocal shva) represents an original vowel that has been reduced to a shortened vowel.
she guarded = שַׁ-מַ-רַ which evolved to the form
שָׁמְרָה

Note on the furtive pataḥ

Section 5.3 of Kelley's Hebrew Grammar explains how the /ah/ vowel must be pronounced before the consonants ח ע הּ (note that the הּ has a mapiq dot inside it.)
But the pataḥ vowel mark should be directly under the letter and not off to the right side of the letter.
Here are some examples:

רָקִיעַ גָּבֹהַ הָרוּחַ