[MENTION=6801328]Elfcrusher[/MENTION]: Here's how I'd most likely do it ...
1) Detecting a Lie: If the NPC is actively trying to deceive a PC, I'd most likely roll the NPC's Deception vs the PC's passive Insight. If, however, the PC's player is actively suspicious of the NPC, I'd most likely roll the NPC's Deception and then ask the player to roll Insight with a DC equal to the NPC's Deception roll. If the player fails, I'd most likely tell them that they can't be sure if the NPC is lying or telling the truth.
2) Being Intimidated: I don't generally roll Intimidation checks against PCs, but if I were to do so, and the NPC were to succeed, I'd most likely just tell the PC's player that the NPC is being intimidating (rather than telling them that their PC feels intimidated). I might add that the NPC looks like they could follow through with their threat of violence or whatever. Basically, I'd try to give the player the impression that going along with what the NPC wants is in their character's best interest without forcing their hand.
3) Using Persuasion: Like Intimidation, I don't generally have NPCs roll to persuade PCs. I usually just have the NPCs state their case and leave it up to the players to decide whether or not their PCs are convinced. If, for some reason, I were to roll Persuasion against a PC, though, I would, again, just say that the NPC's argument is fairly convincing or that it doesn't look like the PC would be able to change the NPC's mind on the subject and should try a different tack. I wouldn't tell the player that their PC is persuaded, though.
Does that make sense?