1.What, if any, connections do you see between learning and computer/video game playing?
Play and learning are very closely related in the human psyche. Play is the innate mechanism by which humans learn about reality. This explains why genuine learning is fun -- it's so close to play. However, schools have managed to take the play -- and therefore the fun -- out of learning. Videogames are extremely powerful educational devices; players learn the game's rules and techniques with amazing rapidity. The problem is, the material they teach is devoid of any socially redeeming value. Oops.
2. What connection, if any, do you see between computer games and the teaching of writing at either the high school or college level?
None whatsoever. Good writing requires mental skills that are absent in computer games. Moreover, such mental skills are at present beyond the reach of our knowledge of algorithmic techniques -- we don't know how to compute good writing. Hence we cannot design any kind of interactive application that helps people learn good writing skills.
3. What do you suppose might be an interesting computer game for the teaching of writing (either currently out or not yet imagined)?
I cannot imagine any such product at the current time. For such a product to be created, we would need algorithms that permit us to algorithmically determine what constitutes good writing. Now, it's certainly possible to create simple-minded algorithms that assess such things as sentence length, abstruseness of vocabulary, even degrees of indirect reference. It's also possible to design algorithms that check for some of the simpler grammatical errors. Thus, it's conceivable that we could create a "good writing" evaluation algorithm that would provide simple advisory commentary.
But the real issues of good writing -- clarity of thought and expression -- cannot be evaluated by a computer and will not be possible to evaluate by computer until computers understand the reality in which people live. The classic example here is the sentence "Time flies like an arrow", which means just one thing to humans but has three possible meanings to the computer, depending upon whether the first word is assumed to be a noun, a verb, or an adjective. Or consider the knowledge of human behavior required to understand this sentence: "I knew my marriage was over when I returned home early from a business trip and found my best friend's car parked in my driveway at 2:00 AM."
So what can be done? Not much. I suggest that you look at my Deikto language system at storytron.com to get an idea of how computers might be used for sentence-diagramming exercises. Perhaps it would be possible to take the old Basic English vocabulary, implement it in something like my Deikto system, and let youngsters play with it to learn the structures of language.