[The Great Eagle Eye]

1. A messenger of love.
Eros, if we mean love of the physical kind.
Cupid, if we mean the cherub of over-priced greeting cards.
Of course, thats only the mystical aspect of a 'Messenger of Love'...

2. Not a rug.
A bear, can be made into a rug, but is not always.
Or perhaps an item involving hair, as a Toupée can be called a rug.

3. Suited for fire.
Wood, it burns well and is suited for fire, or perhaps some kind of armor, if we mean fire in a different sense.