1. How do I discourage players using the knowledge that they have a low roll to influence character decisions?
Be up front and honest with them about not Meta gaming. It is meta-gaming using the knowledge of a low roll to influence your in-character actions/reactions/thoughts/etc. I usually say just what you said, something along the lines of, "You think she seems to be telling the truth." If my player then goes on to think she is lying, I do one of two things:
- Either gently remind them, "Your character thinks she is telling the truth and would not remain suspicious."
- Or, allow them to roll insight again, but on a different bit of information hoping for a higher roll so it's definitive that the NPC is truthful (or not).
The first option is always better, and usually in the long run makes for more engaging role playing when players can accept the cards their characters have been given. One major tip, when they roll low and you tell them they believe the NPC, try not to act devious or suspicious, your tone and demeanor can influence player thoughts tremendously.
2. Should I, and if so how, tell my players if somebody is actually telling the truth even if they have a very low roll to avoid them thinking they are being lied to and their characters are too stupid to figure it out?
This is a bit tougher... first I refer you back to the first part of my answer to the first question. Players acting on the knowledge of low or high rolls in a way that is discordant with the information you give them is Meta gaming. So, if the 2 options above don't work, then you have to ask yourself one question.
"How will having this player remain suspicious of the information affect the narrative?"
This situation is good for on the fly story development!
- The player remains suspicious, doesn't heed the warnings of the NPC and their actions either result in an extremely challenging fight, or worse may even lead to the death of the NPC. This could cause the player to be more careful in the future or become deeply regretful of his stubbornness.
- The player remains suspicious but the NPC pleads with them, "I can tell you don't believe me, and if I were you I might not believe someone like me either... but please good sir knight, proceed with caution!" This could also lead to the outcomes in the previous example if the Player still ignores the warning. Or they may uncover, incrementally, that the NPC was truthful, after which they might go back, apologize and make a new friend.
If the story really is better served with the character believing 100% that the NPC is not lying and there is no in game way to work around the suspicious nature of the player... as a last resort (and I personally would not do this), just tell them out of character that the NPC is being truthful. I can't think of a reason that you would need to have the character believing that the NPC was honest given the ad-libbed scenarios above, but if you find it imperative, it's your call to make.
...and nothing says the player won't suspect you of lying just because you are the DM. ;) Some players will always be suspicious no matter what as they will always believe the DM is "out to get them".
(And to quote another answer here after reading the stuff posted as I was typing this novel length answer... do be up front with your players that anything you say as a DM to the player will always be the truth. Lies might come from NPCs, but never the DM. And always make sure you are consistent in upholding these promises to your players.)
Best Answer
What a PC believes shouldn't be determined by a dice roll.
Instead, give them clues depending on the results of their insight check. For instance, if the PCs are interrogating an NPC regarding a string of robberies, an Insight Check DC10 might allow the PCs to notice that the NPCs eyes widened when shown the torn scarf found at the mayor's house, despite him denying seeing it before (or do an opposed bluff vs insight if the NPC has a very good poker face).
This way, you can play with their perceptions a lot. Maybe the NPC they're talking to knows who this scarf belongs to... or maybe he just realized it was a set-up, as it was stolen from him a few days ago, but would rather deny everything in front of the PCs to take care of the matter himself.
Like in real-life, your players will have to decide what they do with the information available to them. If their Insight check is too low, you might give them only part of the information (the NPC seems to be very nervous, which really could mean anything...), which might in turn lead them to make the wrong decision.
This also seems to be suggested by the PHB (p.178) :
A good insight check should reveal these clues, but the interpretation should be left to the player.
To specifically address the situation of Insight vs. "Not bluffing", you can interpret the insight check as someone trying really hard to find clues about someone's lies. And when they search too hard, people always end up finding something... So if they roll too low, you could just give them wrong cues about the NPC's behaviour (he seems to be sweating a lot... but that's because he was running to get home before his wife sees her surprise birthday gift, which you don't tell them). As to what could be regarded as "too low", there is a very good guideline in the PHB (p.174) to help you set DCs for such tasks.
For example, if you think it would normally be very easy to spot someone's lie (Pureferret's example of a paladin whose very nature is against lies), the DC to notice they are speaking truthfully would be 5. On the other hand, if it would normally be hard to spot the lies (the guy from local fence is so used to lying that you can't really tell if he's lying or not anymore, whether you expect him to or not), then the DC should be 20.
As a DM, it is up to you to set up the DCs for such task. Even if the person isn't lying, success could give some behavioral clues to something else ("he looks distracted, as if he's preoccupied with something else") that could be, or not, a plot hook. On the other hand, failure wouldn't reveal any clues whatsoever, and you could rule that a failure by 5 or more (rolling 15 or under against a DC of 20, for example) leads to wrongful interpretation. For example, when dealing with the guy from the local fence, the PCs are expecting him to lie so much that everything seems to indicate it ("he's never looking at you in the eyes, and often checks down the alley behind you" -- of course! he's dealing with illegal goods and is checking for the town watch!).