No. The next paragraph in the description states:
If the paladin
targets a creature that is not evil, the smite is wasted with no
effect.
The ordering is a little confusing—I think this should be further up in the description—but smite evil has no effect on non-evil creatures, not even bypassing DR.
"Regardless of the target..." refers to and counters "if the target of smite evil is an outsider with the evil subtype, an evil-aligned dragon, or an undead creature..." and not "if this target is evil".
A Paladin's Code always applies, no matter the enemy.
There are many, many arguments about alignment and Paladin's Code enforcement around the internet. The angle that I'm arguing here is not the only valid angle. Others, like the one given in @JackLesnie's answer, are also totally valid depending on your group.
The Code of Conduct Paladin feature says the following:
A paladin must be of lawful good alignment and loses all class abilities if she ever willingly commits an evil act.
Additionally, a paladin’s code requires that she respect legitimate authority, act with honor (not lying, not cheating, not using poison, and so forth), help those in need (provided they do not use the help for evil or chaotic ends), and punish those who harm or threaten innocents.
By a strict RAW reading, the text is pretty clear. If a Paladin lies, cheats, or uses poison, they lose all class abilities. Nothing in the text mentions context or mitigating circumstances, even when you're fighting evil outsiders.
I suspect that this is mainly because Paladins are supposed to not just be Lawful Good, but Lawful Good and then some. A Lawful Good rogue could totally backstab, betray, poison, or lie to a demon without a twinge of guilt or alignment shift, since they are just using the tools at hand to fight evil. A Paladin, however, has sworn to be above that kind of combat, and won't stoop to the demon's level by using dishonorable tactics.
To directly answer your list of questions:
Can a paladin Backstab a demon? No.
Can a paladin lie to a demon? No.
Can a paladin steal from a demon? No.
Must a paladin offer mercy to a demon?
If a demon begs for a fair trial or for mercy (even if the paladin knows the demon will try to escape), must he take the demon as a prisoner and treat it with the due respect to a prisoner? Is "Summary execution" a fair trial enough?
The last two deserve more careful analysis. The Code of Conduct says that the Paladin has to "help those in need (provided they do not use the help for evil or chaotic ends)". If a demon asks for mercy and the Paladin expects the demon to just use that mercy as a way to escape and survive, then they would be using the Paladin's help for evil ends, and so the Paladin is allowed to ignore their plea.
Similarly, if a demon asks for a "fair trial"; Nothing in the Code explicitly states that a Paladin must accept a surrender. Unless there's an overarching legal structure that the Paladin must follow that requires something else, nothing in the Code of Conduct says that the Paladin needs to give a demon anything but a summary execution. After all, the Code says that they have to "punish those who harm or threaten innocents", and killing a demon does just that.
Best Answer
From the Core rules pdf (pg 60):
In the Detect Evil spell it lists a Cone shaped area effect. So my reading of that is that the paladin can do either but not both at the same time. For example a paladin could be talking to three npc's and use the area effect to see if any of them are evil and then after that move is completed on their next movement action focus on one individual to get a full aura reading but then he would stop detecting evil in the area and only focus on that one npc.
Of course it doesn't seem totally clear cut from the rules explanation so individual players/DM may interpret the rule differently.