Why didn't any of the people trapped in the mine area just stack a bunch of boxes and reach that hatch that Phillip entered through?
Do you remember how Phillip opened that hatch in the first place? He had to bash the ice off of it with a rock, anyone trapped below that hatch wouldn't be able to break the ice like Phillip did. That's not even mentioning the trap door below that which could only be opened using a mechanism from above it...
The ice could be melted by lighting a fire under the frozen hatch, and this has been done once or twice in real-life mines in winter. The one-way trap door, though, would require either some serious Mc Gyvering or brute force.
Why did Red wish to die so much in Overture? Why was suicide 'against the rules'?
Because Red was infected with the Tuurngait, a virus that is sentient, and thus probably wouldn't allow its host to commit suicide. And by the time you find Red, he has been trapped for around 30 years. So that might explain what he did.
A note in Black Plague describes suicide under the influence of the Tuurngait as being "against the rules" in those exact works.
Who knocked out Phillip at the end of Overture?
One of the Tuurngait zombies.
If the Amabel monster is just a hallucination, then why is she trying to kill you? Shouldn't it have just stood there or something?
The attack was hallucination, too, obviously. She was rushing to give you the cure or a hug, or something.
Alternatively, Amabel had been turned by the Tuurngait virus and Clarence only made it look like you had murdered her to mess with you.
It's also possible that Amabel used Philip to clear a way out of the facility and once he did that she saw him as hinderence and tried to kill him and she only looked like a monster due to a hallucination. This would explain why she comes across as so innocent yet mildly flirtatious throughout the game despite working in a morally bankrupt science facility. Her sweet personality was just her trying to manipulate Phillip into helping her.
What was the deal with the giant worms? Were they mutated by the Tuurngait? Why?
Eat people most likely. No survivors allowed or word may get to the surface.
What's going on in Requiem? If it is in Phillip's imagination, why is he imagining all of that? If it is real, why does the Archaic have all these facilities?
Could be caused by the madness of being reinfected...
I think it's the afterlife, as characters who died during the previous games are apparently also there.