My guess would be late 14th or 15th century, but that's largely based on weapons and armor.
And no, no one has 11th century armor, unless you interpret what is said in the books a lot differently from me. It seems that most feudal levies/militia wear typical 14th/15th century equipment (polearms, mail+cuir bouilli+partial plate), and retainer troops wear typical 15th/early 16th century armor (full plate, close helms, great lances, etc..). There are quite a few anachronisms not unlike the kite shields, but I suppose that could be explained away as:
1. GRRM messing something up (e.g., he might've confused kite shields with heater shields).
2. GRRM not caring or knowing something.
3. Vikings. Vikings with plate armor.
As far as society goes, it really could be anywhere. Although with the free cities, tech levels and some offices (like king's hands, maesters) I am more inclined to believe it's later middle ages.
As for the second request, to help you picture the troops, I suggest this system - view northmen as Scots/Irish, the rest of the continental Westerosi kingdoms as English/French/Germans, except for Dorne - which could be Spain, view the Ironborn as vikings (well, duh) and the free cities as a bastardized version of Italy. Pictures:
1. Professional infantry men-at-arms from the private retinues of nobles, as well as dismounted knights and nobles themselves:
1.5 Mercenary companies/retainer specialist troops:
2. Nobles, their retainers and knights:
3. Yeomanry (free landholders outside the basic feudal structure) and townsmen militias (the most common types of troops in an army along with larger retinues and free companies)
^note that the above two images seem to misrepresent brigandines and a few other things.
4. Peasant conscripts (used in desperation and for stuff like supplying the army, guarding said supplies and acting as arrow-fodder during sieges):
ETA: Pictures won't show so I made them links instead.
Edited by Darth Rivers, 26 March 2012 - 10:18 AM.