In the beginning

Let's get down to business...Do fairies and elves exist? Are they a figment of our imagination? 

From as long ago way back in Chaucers time the tale of Wife of baths tale *1387/1400 

In olde dayes of the king Arthour,
Of which that Britons speake great honour,
All was this land full fill'd of faerie;* *fairies
The Elf-queen, with her jolly company,
Danced full oft in many a green mead
This was the old opinion, as I read;
I speak of many hundred years ago;
But now can no man see none elves mo',
For now the great charity and prayeres
Of limitours,* and other holy freres, *begging friars 2
That search every land and ev'ry stream
As thick as motes in the sunne-beam,
Blessing halls, chambers, kitchenes, and bowers,
Cities and burghes, castles high and towers,
Thorpes* and barnes, shepens** and dairies, *villages 3 **stables
This makes that there be now no faeries:
For *there as* wont to walke was an elf, *where*
There walketh now the limitour himself,
In undermeles* and in morrowings**, *evenings 4 **mornings
And saith his matins and his holy things,
As he goes in his limitatioun.* *begging district
Women may now go safely up and down,
In every bush, and under every tree;
There is none other incubus 5 but he;
And he will do to them no dishonour. 

The Fae was distinctly mentioned in this poem. So, are we to believe they exist?

YES of course they do, open your imagination and let us see them for ourselves.