шум - is like noise in the broader fuzzy, perhaps elongated sense. Like the "noise" in "white noise", but not really any single sound.
звук - is a sound, more of an isolated event. In English we refer to this with "a noise" sometimes, or "a sound"

If you somehow drew 2 conceptual venn diagrams over each other representing English sound vs noise and Russian звук vs шум [so four circles], NO circle would quite line up with any other one.

Шарить в поиске/поисках + genitive -- that's a brilliant way, yeah. "To rummage in search of something"

That is a great site!

Learning "for" is a fairly insanely complex topic, definitely not something one can grasp after just one day.

Seeing examples definitely straightens things out over time.

они́ гото́вятся к экза́мену‎ ; preparing for the exam

Приготовьтесь к битве - prepare yourselves for battle

Yup yup, у on наверху is a representation of locative, basically modern prepositional, distinguishing against наверх, which would be accusative верх.

In perfect theory, commas aren't used to distinguish concepts, just to mark barriers. [in reality, well, things happen]
Anyway, the comma doesn't affect свой's destination, it aligns with the subject regardless of distance and whatnot. этаж is brought up as something other than the subject of the sentence, so to refer to its possessions you'd use его ____.

'я достал в кармане для ключей, чтобы поискать ключ инженера для доступ на запретный этаж наверху и свой аппарат.

That's свой's job, it is irrevocably linked back to the subject, and intentionally marks a distinction if его is used instead.

Его could technically refer to the "engineer's" or the "floor's", context governs here, so a total rephrasing of the sentence would yield clearer boundaries for sure.