The Moody Bible Commentary (MBC), which is dispensational, pre-tribulation, and pre-millennial in its outlook, takes an in-depth look at these verses. Some relevant points from it include 1) the rapture is described as a single event and 2) the distinct steps of the event do not suggest a delay.
1) The commentary describes the rapture multiple times as a single event, distinct from Christ's second coming. Describing Paul treatment of the subject, MBC reads, "[h]e dealt with the persons involved, the plan of the event, and the point of his teaching." MBC contrasts this rapture event with
the event described in Mt 24:31 where, at the second coming, the angels will "gather together His elect." Thus, there are two distinct events associated with the parousia—the rapture and the second coming (or "revelation") of Christ. [bold emphasis added, italics in original]
2) MBC summarizes the sequence of the rapture as first the descent of the Lord, then three distinct sounds (shout, voice, and trumpet), then the reunification of the souls of the dead in Christ with their bodies, then the taking up of living believers. One point in particular touches on your questions regarding the sounds and the timing:
The exact nature of these sounds [shout, voice, trumpet] is unclear, but apparently the purpose is to summon believers and signal that the blessed hope is about to be realized.
In this quote we see that the sounds are a) for believers only and b) that they indicate the imminence of the catching up. MBC continues:
Then, living believers will be caught up (v. 17) along with those resurrected saints. The nature of the event is indicated by the term harpazo, which means "to grab or seize suddenly so as to remove or gain control, snatch... [or] take away." [emphasis in original]
Here we again see the emphasis on the sudden nature of the event, but even more clearly than before, the singular nature of the "catching up" event (resting on the text of verse 17, "caught up together with them in the clouds").
To summarize, the Moody Bible Commentary describes the rapture as a single event consisting of several steps immediately following one another, and suggests that the sounds associated with the rapture are meant to call believers.