I would say "not necessarily inspired" or "not generally inspired" because I wouldn't want to rule out the work of the Holy Spirit in a translator's life and work any more than I would want to rule it out in the life and work of a scientist or school teacher or farmer.
See my qualification on "the process of translation" just above.
Sometimes. Other times, there can be no denying the intended meaning. For example, no one thinks that the New Testament declares someone other than Jesus to be Lord.
I'm not as dismissive of the statement as you are, but I seldom, if ever, use it myself, and while I think it's an acceptable way for someone to raise an issue, I don't think it's an effective way to settle an issue.
I might agree with this statement and I might not; I just don't fully understand it. I suppose its meaning turns on your definition of "new" and "doctrine."
See my comments on "the process of translation" above. I think of theology as the body of man's thoughts about God; the more of God's thoughts we can make a part of it, the better. Therefore, I don't rule out the possibility that a theological thought can be inspired.
I hope this demonstrates why I said I shared your assumptions in general terms and would only vary in some particulars.