The alarm's bell cut through the silence of the stale, dark room, audible from a phone which was based on a wooden nightstand.

A darkroom is a room for developing photos - I believe you mean simply a room that is dark.
"Audible" is slightly awkward but works.
Same for "which was based on" - I would probably say "that stood on", or "that lay on".

Near it was an old, bed that squeakinged with the slightest touches bed, upon which lay, a seemedingly dead body.

Or "a body that seemed dead". "Upon" instead of "on" is not very important.

The young woman lay around in bed, hugging her toy's shark.

"Her toy's shark" means the shark that belongs to her toy.
I can't exactly explain why "lay around" feels wrong, but it does.

SIt seemed like nothing could ruin her sleep, except bythe ringing of a mobile device.

"Mobile device" is awkward here, you'd probably just say "phone".

Perhaps, that action was completely nonsensical, because she was in her house, in the place, which isa place most people would called safe.

I choose "most people" because in the next line you talk about how for her, the house is not safe. You could say "a place you would call safe", or "a place anyone would call safe". It would be more natural to say something like "a place where most people feel safe", but "call" works.

But not for her, it wasn't.

Very minor.

Every time, when she wakes up, she automatically does the same actionthings: looking around, sniffing, doing alleverything to make sure that she i's out of danger.

I change "actions" to "things" because it's strange to talk about "doing an action". You are more likely to "do a thing", "do something", or "perform an action".