I'd like to ask you a few more questions related to A Song Of Ice And Fire: Are the archers from the eastern continent generally more skilled than their Westerosi counterparts?
No, though they have different fighting styles. Horse archers are more common in the east.
How about their bows? (effective/theoretical range, strength, etc.)
The best bows are made of the golden wood from the Summer Isles. The Summer Islanders are probably the best archers in my world.
I presume the mounted mercenaries from the eastern continent aren't as heavily armored as the Westerosi knights? What about their skills and discipline compared to the Westerosi knights?
It varies. Some of the sellsword companies are very disciplined, and some are nothing but rabble joined together in search of loot. At one end there would be the Golden Company, at the other the Brave Companions. The Second Sons and the Stormcrows are in the middle.
What is the general composition of the Westerosi armies? My impression is that the knights or mounted men represent the back-bone of their armies.
They are certainly the most feared component, yes.
What is the relative composition of archers (or horse-archers), infantry and cavalry?
Infantry outnumbered cavalry by a considerable margin, but for the most part we are talking about feudal levies and peasant militia, with little discipline and less training. Although some lords do better than others. Tywin Lannister's infantry was notoriously well disciplined, and the City Watch of Lannisport is well trained as well... much better than their counterparts in Oldtown and King's Landing.
Will they be able to support their armies with larger groups of archers (say, thousands of archers) in an effort to withstand or prevent attacks from flying dragons?
If they can find thousands of archers... depends on the season, of course...
Dany's planned invasion of Westeros looks very interesting from a military standpoint. Do you perchance model battles, tactics or campaigns in ASOIAF after historical battles or campaigns, or do you mix ideas from different battles/campaigns?
I make it up as I go along. Mix and match actual battles from history, but with a certain amount of imagination and invention thrown in.
Have you studied the campaigns of, say, Hannibal, Caesar, Napoleon, Scipio Africanus or Alexander the Great?
To a certain extent, yes. I wouldn't call myself an expert, by any means, but I've read all the biographies, I've got a lot of Osprey books, and I have read Keegan and Norman Dixon and Fletcher Pratt.
Will Dany continue to strengthen her 'army' of mercenaries and Unsullied by adding more cavalry and archers? I read in one of your officially published emails that a larger merc group will appear in A DANCE WITH DRAGONS. Is this group related to Dany? (I guess this is a potential spoiler-question, so I understand that you might not be willing to answer this question.)
You'll need to wait and see.
I'm a bit concerned about Dany's skills as a commander. To succeed with the invasion of Westeros, I believe she will need a lot of sound military advice (both tactically and strategically). What's your thoughts on this issue?
She will need counsel, yes... she will also need to learn to tell the good counsel from the bad, which is perhaps the hardest task of all.