"The Stone City" was actually one of the best SF stories I ever did. Nice that it's still remembered. I published it myself in NEW VOICES I, which perhaps doomed it to obscurity. To tell the truth, I don't recall what a Damoosh looked like. A Hrangan Mind, on the other hand, I remember very well... but whether I will ever bring one on stage, I don't know.
As to whether I'll ever finish AVALON... well, perhaps. Hard to say. Just now I am not looking past A SONG OF ICE AND FIRE, which is likely to occupy me for five more years at least.
Let me answer some of your questions about the fantasies...
[Note: Some time later, in separate correspondence, GRRM described Blackfyre as a hand-and-a-half sword rather than a greatsword.]
Targaryen bastards have been given a number of different names over the years. The Blackfyres are one specific branch, descended from Daemon Blackfyre, a bastard son of Aegon IV the Unworthy by one of the three sisters that Baelor the Blessed imprisoned in the Maidenvault. Blackfyre was also the name of Aegon the Conquerer's greatsword, a fabled blade of Valyrian steel passed from king to king... until Aegon IV chose to bestow it on Daemon instead of his legitimate son, Daeron, whom he suspected was actually fathered by his brother, Prince Aemon the Dragonknight. Some felt that the sword symbolized the monarchy, so the gift was the seed from which the Blackfyre Rebellions grew. None of this is in the books as yet, but it will be revealed gradually in future volumes.
The Freehold of Valyria is correct. Valyria at the zenith of its power was neither a kingdom nor an empire... or at least it had neither a king nor an emperor. It was more akin to the old Roman Republic, I suppose. In theory, the franchise included all "free holders," that is freeborn landowners. Of course in practice wealthy, highborn, and sorcerously powerful families came to dominate.
[GRRM is asked about Sansa misremembering the name of Joffrey's sword.]
The Lion's Paw / Lion's Tooth business, on the other hand, is intentional. A small touch of the unreliable narrator. I was trying to establish that the memories of my viewpoint characters are not infallible. Sansa is simply remembering it wrong. A very minor thing (you are the only one to catch it to date), but it was meant to set the stage for a much more important lapse in memory. You will see, in A STORM OF SWORDS and later volumes, that Sansa remembers the Hound kissing her the night he came to her bedroom... but if you look at the scene, he never does. That will eventually mean something, but just now it's a subtle touch, something most of the readers may not even pick up on.
[Note: Compare the remarks on Nymeros Martell to this later statement.]
You ask about names. Several different questions here. Maege Mormont is called Mormont because no one knows her husband's name, or even if she has one. There is all the talk that she beds with a bear. She prefers to keep her own counsel. Most of the ladies of Westeros do change their names when they wed, although usage varies. If the wife's family is significantly higher born than the husband's, she may use his name little, if at all. The Dornish have their own customs. The full surname of the ruling house of Dorne is Nymeros Martell, and the ruling pricesses keep that in its female form. They do not take the name of their consorts.
Bastard names are given only to bastards with at least one parent of high birth. So the bastard child of two peasants would have no surname at all.
Thus a bastard name like "Snow" or "Rivers" is simultaneously a stigma and a mark of distinction. The whole thing with bastard names is custom, not law.
The highborn parent can bestow the usual name, a new one of his/her own devising, or none at all. Most legitimate sons of bastards keep the bastard name, but there are cases where a later generation fiddles with it to remove the taint. There's one such case that you will meet in the next book, a minor character descended from a Waters (a bastard name along the shores of Blackwater Bay) whose great grandfather changed the name to Longwaters for just that reason.
Maester Aemon is doubly sworn, to both Citadel and Night's Watch. That is true of the maesters at Eastwatch and the Shadow Tower as well.
[GRRM is asked about Shae being in Tywin's bed.]
I won't comment on the Tyrion / Tywin issue. Perhaps future volumes will throw more light on it.