The basic unit of English grammar is the clause. Generally, speaking a clause has a subject (roughly the person or thing that the clause is about) and a predicate. The predicate contains the verb (roughly the words telling us about the state of or the action taken by or applied to the subject). The predicate also contains complements, those elements needed to complete the sense. Both subjects and predicates may contain adjuncts, which supply additional information.
When a clause contains a finite verb, (i.e., a verb carrying tense, which tells us about time -- past, present, or future) and contains a complete thought, then we have a sentence. Let's look at a simple example.
[1a] She is a famous woman.
[1b] She was a famous woman.
1a and 1b are both sentences. They each convey a complete thought with a finite verb. The verb in each case is a finite form of the verb to be. In 1a the tense is present; in 1b, the tense is past. In both sentences the subject is the same, the pronoun she, and each sentence has a complement, woman, and that complement has an adjunct, namely the modifier famous.
But clauses don't have to have finite verbs. Consider the following clause:
 you being a woman
Example 2 is a clause. The subject is the pronoun you, the complement is woman, the adjunct is the indefinite article a, modifying woman. But the verb is nonfinite. It's the present participle of the verb to be, which carries no tense. We don't know when the person being addressed had the characteristic of being an adult female. Therefore, 2a doesn't express a complete thought in English and isn't a sentence.
In simple clauses, nouns and pronouns take the role of subject (you in the examples), and complement (woman in the examples). Adjectives take the role of adjunct to (modifier of) nouns (e.g, the word beautiful in the phrase "beautiful woman"), and adverbs take the role of adjunct to verbs and adjectives (e.g, quickly in "run quickly" or very in "very quickly"). Prepositions combined with their complements are also adjuncts, telling us mainly about place and time.
But English allows whole clauses to play the same roles mentioned above. This allows for the construction of complex sentences expressing complex thoughts. And that's what is happening in your example, all of which are nonfinite clauses with being, the present participle of the word to be. When this type of participle plays the role of a complement, the way a noun would, we call it a gerund.
Verbs in nonfinite clauses are different from verbs in finite clauses. Remember that the latter play a role in predicates and have tense. Am/Is/Are are tensed forms of the verb to be and are appropriate as a predicate's verb but not as a verb form in a nonfinite clause.
Here's one of your examples, with a parallel construction not using a nonfinite clause.
[3a] She was afraid of being late for Matins.
[3b] She was afraid of lions.
In 3a, the nonfinite clause being late for Matins is the object of the preposition of just as in 3b, the noun lions is the object of the preposition of. Both serve to tell us what she feared.
[4a] No one knows how he escaped being dashed to pieces.
[4a] No one knows how he escaped death.
In 4a, the nonfinite clause being dashed to pieces serves as the direct object of the verb escaped, just as the noun death serves the same purpose in 4b.
You didn't give an example, but nonfinite clause may play the role of the subject in sentences. Consider
[5a] Being late for Matins made her afraid.
[5b] Lions made her afraid.
The subject, i.e., the thing that does the fear making in 5a, is the nonfinite clause in bold, just as in 5b, the noun lions is the the thing doing the fear making.
The present participle can also be an adjunct, acting as a modifier. That's what's going on in your example
[6a] Now, think about everything being recorded.
[6b] Now, think about everything beautiful.
In 6a, you're told not to think about everything, just those things being recorded. The nonfinite clause being recorded limits or modifies the noun everything, just as in 6b, you're told to think of just those things limited by the adjective beautiful.
Warning: to say this answer simplifies English grammar is an understatement. It is only the barest of explanations and skips over many topics. For instance, I say that clauses have subjects, but you may have noticed that the gerund clause in 3a doesn't have a stated subject, but it does have one that can be recovered from the sense: the person being late for Matins is the same one who is afraid. Exceptions are numerous, complexities abound, and not everyone agrees on terminology and analysis.