What does 'otherwise' mean?
Our sense of how deprived we are is relative. This is an observation that is both obvious and (upon exploration) deeply profound, and it explains all kinds of otherwise puzzling observations. Which do you think, for example, has a higher suicide rate: countries whose citizens declare themselves to be very happy, such as Switzerland, Denmark, Iceland, the Netherlands, and Canada, or countries like Greece, Italy, Portugal, and Spain, whose citizens describe themselves as not very happy at all? Answer: the socalled happy countries.

2nd line 'otherwise' means:
1. if our sense of how deprived we are is not relative or
2. if an observation is not obvious and profound

I read over and over again, but I'm confused.

Question

What does 'otherwise' mean?
Our sense of how deprived we are is relative. This is an observation that is both obvious and (upon exploration) deeply profound, and it explains all kinds of otherwise puzzling observations. Which do you think, for example, has a higher suicide rate: countries whose citizens declare themselves to be very happy, such as Switzerland, Denmark, Iceland, the Netherlands, and Canada, or countries like Greece, Italy, Portugal, and Spain, whose citizens describe themselves as not very happy at all? Answer: the so­called happy countries.

2nd line 'otherwise' means:
1. if our sense of how deprived we are is not relative or
2. if an observation is not obvious and profound

I read over and over again, but I'm confused.

Answer

'Otherwise' means 'in another way'; in this case 'the other way' would be: without the previously mentioned sentence which states that: 'our sense of how deprived we are is relative'.
I will rewrite that sentence substituting the word 'otherwise' with other words in capital letters, so that you can understand:
...and it explains all kinds of observations WHICH WOULD BE puzzling WITHOUT THE OBSERVATION WHICH STATES THAT: 'OUR SENSE OF HOW DEPRIVED WE ARE IS RELATIVE'.

Answer

Means differently or oppositely confusing observations, unlike the example that is explained in the passage which is described as obvious and deeply profound.

Answer

The observations are puzzling unless we realize that "our sense of how deprived we are is relative."

Answer

'otherwise' is not in the 2nd line, though.
it means that 'if we don't realize that our sense of how deprived we are is relative'.
'otherwise' puzzling observations = puzzling observations 'if we don't realize that our sense of how deprived we are is relative'
hence '1. if our sense of how deprived we are is not relative' is correct.