Sun Appearing to have Stopped Shining
This is arguably a theological rather than science-based issue, but since it is cross-cutting I will answer it. No, there is no possible mechanism for the sun to cease shining for three hours, but neither is there any such imperative implied in the original Greek text, which requires only a relative darkening of the sun. You are correct is recognizing that this was no eclipse. It may be noted that comparable 'darkness' is implied in other Biblical accounts, such as in Exodus, Joshua and Amos. Nowhere in these four texts is total darkness either stated or implied, but naturalistic explanations (i.e. scientific) - which in no way detract from the spiritual intent of the text - may be eminently applied to correct textural understanding.

As in so many modern misunderstandings, the apparent conflict between science and Biblical theology entirely disappears when the Bible is read sensibly from the appropriate perspective. The Bible is not a modern Greco-Roman literalist quasi-scientific text, and it is absurd to treat it as such. the Bible is basically a spiritually-inspired collection of 2000 to 3000 year-old Hebrew texts, written in the parabolic allegory-rich idiom of ancient Jewish culture. For all that, it is no less accurate in spiritual wisdom - but radically different from the 21st century world views. 
Not only is it literature from a different culture, we also don't have any of the original texts! You are arguing on the basis of a modern British translation of a Greek translation of presumed Aramaic literature, which itself may have undergone several cycles of editing (as in the Noah story, which has at least four cycles of precursor literature).  Subtleties of meaning are lost in each stage of translation, so before drawing over-literal assumptions, first at least check the nuances of the earliest Greek translation. Had you done that, the question of absolute darkness would not have arisen, and partial darkness would more than adequately have proved correct - such as a sandstorm (as 'A child of God' suggested) or a super-cell storm cloud - which does occasionally occur in the Israeli highlands. Such superstorm events may indeed seem to be like night if they occur only minutes after the intense bright Mediterranean sunlight of the Jerusalem highlands.

Many Christians get hot under the collar when scientific explanations are applied to miracles such as this. It need not be so. It is not a case of "look at God doing the impossible, again", but of placing due emphasis upon the true miracle, which is the exquisite timing of the event in support of God's unfolding plan.