Sarcoth: Thanks for starting this thread! It's extremely informative, having a chance to see the ways that others would deal with this situation. All the people that I game with have, over the years, developed pretty much parallel concepts on the alignment issues, and it's fascinating to see how people with differing views on the question would respond.
Now, to address your questions:
Situation A: The group is attacked by a group of thieves right outside a city. The thieves are easily subdued. Some are unconscious and bleeding to death.
Question 1: What should the healers do?
LG = The correct response varies depending on the laws of the kingdom where the assault took place, which my lawful good character would have made an effort to learn in essence as soon as entering the kingdom. Assuming typical laws, the dying thieves should be stabalized, and the entire group should be securely restrained.
NG = The dying thieves should be stabalized, and all the wounded treated to ease their pain. The thieves should be securely restrained, and the leader, if identifiable, should be healed to the point where he can be interrogated, using magic if necessary. He should be carefully questioned - using magic to prevent deception, if possible - to determine his and his followers motives. The proceedure from that point would be contingent on what was learned from the interrogation.
CG = This would vary considerably depending on the individual motivations of the character in play. At the very least, the thieves would be stabilized. Some CG characters might try and reform / convert / recruit the thieves, in the hopes that they may learn a better way of life.
Question 2: Should the group take prisoners and turn them in at the local guard?
LG = Almost certainly; local laws may, of course, provide otherwise.
NG = If the thieves prove to be acting from simple criminal motives, yes. If they are acting from need or due to poor circumstance, most likely not.
CG = Only as a last resort - the local law enforcers will not likely do anything to make the situation better, regardless of the circumstances.
Situation B: The group is attacked by 2 Fire Giants. One is taken down and then the other cries surrender.
Question 1: How should they react?
LG = Unless doing so will almost certainly compromise the surviving party members, the giant's surrender must be accepted. It would not be improper to place conditions on accepting the creature's surrender, however.
NG = If the party is able to defend themselves adequately from the surviving giant, then accept the surrender long enough to negotiate terms. Otherwise, or if the giant refuses to accept equitable terms of surrender, subdue it.
CG = Again, the reactions depend on the particular character. In general, if one or more party members were killed by the giant, refuse the surrender, and kill it. Other reactions, depending on circumstance, would include accepting the surrender or subduing the giant.
Question 2: The group paladin already determined they were evil. Would this change how the group should react?
LG = Most likely, no. Very few lawful societies prosecute creatures based on how they detect to divination magic. Some exceptions are obviously possible, however.
NG = If the creature has been unequivocably identified as evil, then it is probably best to subdue it first and ask questions later, rather than accepting its surrender. Evil creatures are, in general, treacherous and untrustworthy.
CG = Perhaps; as usual, its a matter of circumstance and the character's personal motivations.
That's my 2 cp. for now.