1)
I have no head, and a tail I lack,
But oft have arms, and legs, and back;
I dwell in the palace, tavern, and hut -
It's a meager residence where I am not.
If a king were present - I tell you no fable,
I still should be placed at the head of the table.

2)
A word that's composed of three letters alone,
And is backward and forward the same;
Without speaking a word makes its sentiments known,
And to beauty lays principal claim.

3)
The reverse of fourteen,
The extremes of eleven,
Unite them and she'll tempt
Six men in seven.

HINT:
3. Part of the answer uses Roman Numerals.

Answers:

1. Chair 
2. Eye
3. VIXEN