I think it's okay to use правильный or подходящий, not sure.
Here's how that first bit reads to me:


я достал из кармана ключи, чтобы искать А и Б

А) ключ инженера для доступ на запретный этаж кверху/наверх [Idunno which, but not сверх; that one is a preposition],
Б) свой аппарат

So one half of the meaning of the sentence is:

я достал из кармана ключи, чтобы искать свой аппарат
I pulled the keys out of my pocket, to look for my device

свой feels like it is going back to Я.
If you meant the этаж's device I definitely think его аппарат.

I'd flip the order of за мной and кашлянул. [MasterRussian has a page on "Theme and Rheme" discussing word order effects, Lesson on Russian Sentence Structure ]

In my experience Russian doesn't use для as an arm for verbs, so to speak; whereas English uses "for" after many verbs, not only does Russian split "for" into a few different variations, it doesn't use them as object facilitators nearly the same. Most straightforward example is "to wait for"
ждать + genitive , no preposition "for" needed
искать + accusative [the sentence you used поискать and для is a different, and okay in this respect]

It's common to see prepositions like к, на, над, в, об used in conjunction with verbs to direct their meaning, but для seems to be in a generally different camp.

The part I'm questioning is "шарить для чего-либо". I don't know enough about the verb шарить to tell you how it IS supposed to used. Without any other suggestion, I'd just assume шарить + accusative is correct.

Он оттолкнул девочку и начал ловко шарить в карманах у солдата.

...

по карманам is a common phrase added to the verb... Meaning basically "To rummage around inside something"

Зачем ты шаришь по моим сумкам?

...

I can't find a phrase that includes an object of шарить.

обшарить что-либо means "to rummage through something", without any preposition...

Бородатый с беспокойством поднялся, обшарил глазами толпу.

Yeah, so I can't find and "to rummage after something". Для seems bad, not really what that version of "for" does. I guess, on a limb here, you might be able to say
шарить за что-либо to say "rummage for something"

Edit: Nevermind. Post above this explains
Anywho, I just found https://wikivox.ru/предложения-со-словом/ , which seems to be a fantastic source for understanding a word's grammatical ports, because it gives you a bunch of native full sentence examples.