The whole thing is predicated on having a Catholic confessional state where heresy is causing a major disruption in the social order. Hence the Inquisition's lack of jurisdiction over anyone who wasn't Catholic. I don't think anybody could or would justify this kind of system now, regardless of what the punishment measures were.
In fact, I'll go so far as to say that it would be outright condemned in a place like the US because trying to impose this on such a pluralistic society would create such upheaval.
On the other two. I'm assuming you'd agree that purely ecclesiastical punishments would be ok. Yes, given the circumstances back then, I think that civil punishments were licit. Capital punishment? No.
Of course, sometimes heresy might be a motive for another crime, which might open you up to the death penalty.
Ultimately, I can't say the Inquisition is some kind of intrinsically bad thing. It's abuses were bad, but the notion of a confessional state that has deemed heresy a crime to have separate courts for determining if a crime has actually been committed is going to yield better results than the alternative.