Meaning in Context – What Does ‘Check It Out’ Mean?

The book has "flying glass" in bold because it is a heading, and the following checklist pertains to it. In an earthquake, windows and mirrors can shatter, and the force could cause the broken glass to fall at an angle, not just downwards; this is why it is referred to as flying glass.

Anything that is projected into the air could have the verb "to fly" associated with it. For example,

"As I walked through the park, I saw children having a snow fight. Soon afterward, there were snowballs flying all around me as I rushed to get past."

A door is the wood panel with a knob or handle that you open to enter and exit a room. A doorway is the framed opening that the door is mounted to.

As to why a doorway is a safe place during an earthquake (or even if it is), I found conflicting results when I searched for an answer. This article suggests that crawling under a table is more safe:

DO NOT stand in a doorway. You are safer under a table. In modern houses, doorways are no stronger than any other part of the house. The doorway does not protect you from the most likely source of injury−falling or flying objects. Most earthquake-related injuries and deaths are caused by falling or flying objects (e.g., TVs, lamps, glass, bookcases), or by being knocked to the ground.

As discussed in the comments below, the safest place for an earthquake depends on several factors, so please do the necessary research for your area.

Google Books claims 2,850 hits for crawl out of my skin, so I guess that's common enough to say it's an "idiom". I doubt many if any of those hits are literal usages (a Wild West trapper waking up and crawling out of the bearskin he slept in, for example). It just means to feel so (psychologically) uncomfortable that you wish your conscious mind could somehow escape / slink away from your body.

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