If something takes guts, it requires courage in the face of danger or great risk. It takes guts for firemen to enter a burning building to save someone.
If you turn the other cheek, you are humble and do not retaliate or get outwardly angry when someone offends or hurts you, in fact, you give them the opportunity to re-offend instead and compound their unpleasantness.
You you are up to your eyes in something, you are deeply involved or to have too much of something like work.
('Up the neck', 'up to the eyeballs' and 'up to the ears' are also used.)
This is from The Rime of the Ancient Mariner, a poem by Samuel Taylor Coleridge, and is used to suggest that despite being surrounded by something, you cannot benefit from it.