Partial Findings -

First letters of first part gives NAPE(Which is back of a person's neck)

Now twenty sixteen has faded away:
A terrible year, I really must say.
People dying, relationships up messed,
Elections and politics dividing the West.


Taking first letter of the last part gives THROAT

The above is a riddle to future from past.
Here's to a better this year than last.
Riddles and challenges must be solved
On this great site, so far evolved.
And to all of you, my wish for this year:
That you find fun and ne'er shed a tear.

Partial Findings -

First letters of first part gives NAPE(Which is back of a person's neck)

Now twenty sixteen has faded away:
A terrible year, I really must say.
People dying, relationships up messed,
Elections and politics dividing the West.

I think the middle part gives on

I turn over on my side, -> on is turned to no
For all is upside down. -> ou is upside down of on
I piss again and again,
But really, why bother?
Just west of north, -> West of north but backwards
I exist, but backwards.
Now you are here, -> Twice Here
Coming twice for me.


First letter of the following part gives - A FEW
Why do we do it?
Existential crisis!
For all is wrong again,
And we must fill the gap.


Taking first letter of the last part gives THROAT

The above is a riddle to future from past.
Here's to a better this year than last.
Riddles and challenges must be solved
On this great site, so far evolved.
And to all of you, my wish for this year:
That you find fun and ne'er shed a tear.

So..

I get NAPE ON A FEW THROAT which may or may not be the final answer :)