First of all, there is no one Bible. The Protestant and Catholic Bibles are not exactly the same, and there are different translations with different interpretations of the text. Generally speaking, it is appropriate to use the Bible as an authoritative source of what is in the Bible (e.g. the King James version). Different religious sects debate the significance of biblical passages all the time, and it is fair game for them to wave Bibles at each other.
That really depends on how the theist uses it. If the debate is over what the Bible says, then yes. For example, one could have a debate over whether the Bible makes a specific prophecy and whether or not it came true. On the other hand, quite a few theists are so used to quoting scripture to each other in religious debates that they seem incapable of communicating a point without quoting scripture. Atheists see the Bible as a mixture of historical records and religious folklore, so quotes from scripture do not have the same effect on them as they do on believers. I am always put off when someone starts throwing out Bible passages in the middle of a debate, as if the arcane biblical language were somehow more comprehensible than a simple paraphrase in modern English.
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