You say that the network fee will soon become 0. Won't that mean that some people will start registering every word in the dictionary because it will be very cheap to do so (the only cost will be possible transaction fees)?
I didn't say it will become 0 soon. Look at the formula and do the math of how much time it will take to reach that point.
Shouldn't the price at any point in time be at least the USD equivalent of, let's say, 1 USD to prohibit domain squatters?
It is impossible to predict the future value of NMC. Also it is impossible to predict the future purchasing power of 1 USD, it might become too high or too low at some point.
What happens if it turns out that there will be no need for transaction fees because enough miners choose to handle all transactions for free? Then it would be totally free to register as many domain names as one would wish, right?
Sure, but since blocks have a size limit those transactions would probably stay in limbo forever because of their low priority. People will willingly pay transaction fees in order to be first in the line.