(If a Paladin must grant mercy to every one that asks for it and the bad guys know this then every bad guy will of course ask for it, and use it to manipulate the Paladin, maybe to avoid the Paladin from shooting him with a bow as he's escaping yelling "I beg for your mercy oh mighty one, you wouldnt shoot me in the back would you, your righteousness?.") In our campaign the Paladin takes the shot every time
The Book of Exalted Deeds says in pretty clear and explicit terms that, yes, a Paladin MUST grant mercy every time. Now, this would be enough to cause even me to stop playing Paladins, but fortunately, they give you a new use for the Diplomacy skill, which gives the Paladin the chance to redeem the captured villain. Changing his alignment to Neutral, and possibly even Good (I.E. Say you capture an Orc. You can potentially change his alignment from Chaotic Evil to Chaotic Neutral or even Chaotic Good). That, IMO, offsets the whole "must grant mercy" schtick. So all you really need is for you and your DM to have an understanding that he shouldn't have villains asking for mercy unless he REALLY wants to see the game tied down with the reformation of that villain. Besides, any DM worth his salt wouldn't have villains asking for mercy all the time, with the PC's having to travel with 30 prisoners in a chain gang, so it's not something one really needs to worry about. Besides, I personally like the idea of redeeming the occasional villain.
A Paladin can ambush an known evil doer with deadly force. This would be reserved to evil outsiders, evil clerics etc.
I take it you mean a Paladin can NOT ambush an evil doer with deadly force? Well, if the question is regarding Sneak Attack, then both Book of Exalted Deeds and the Complete Adventurer answer this question in a roundabout way. In Book of Exalted Deeds, which goes into pretty heavy depth as to what's okay for the Exalted (All Paladins are Exalted, btw) character and what isn't, and nowhere is Sneak Attack mentioned as the action of a dishonorable character. In addition, they have a statted NPC who's a Rogue 3/Paladin 1.
Secondly, Complete Adventurer features several options for the Paladin who wants to have Sneak Attack. They have a Feat which allows for a Paladin to freely multiclass with the Rogue class, as well as a Prestige Class called the Shadowbane Inquisitor, which not only advances Sneak Attack damage, but can also freely multiclass with the Paladin, AND allows the Paladin to freely multiclass with the Rogue. So to sum up, it appears that Sneak Attack isn't a problem.
He must challenge the Blackguard anbd give him time to arm hiself
"Why you cowardly son of a bitch. You just sneak attacked an unarmed orc!"
"Well, then, he should've armed himself ... if he's gonna decorate his armor with my friends scalp."
This is a tough one, but once again, I don't recall anything being said about not being able to attack unarmed enemies, so long as you KNOW they've done something wrong. You can't just attack someone for BEING evil, but you can attack them for DOING evil.
Anyway, I suggest picking up the Book of Exalted Deeds first chance you get. It really is the best source when it comes to defining what a Paladin in specific, and Exalted characters in general, can and can't do.