Your two example situations doesn't seem like tricking someone into lying so much as lying to someone to promote them to lie in return. Especially the second one - I would not look kindly on someone who trashed me just to get someone else to admit that they did something bad to me too. There has to be a better way of going about it.
I don't think it is promoting them to lie, though. If Person B really did hate Bob, but had nothing to do with framing him for anything, wouldn't they just say, "Yeah, I hate Bob too!" Why would they say they framed him?
I think that is what bothers me about your examples - if the person isn't lying or didn't do what you suspect them of what has it gained you? Especially in the second instance. Is Bob supposed to believe that you didn't mean to trash talk him - that you just wanted to get a confession from someone else? And just because they don't confess to doing it doesn't mean they didn't do it - they could just be smart enough not to blab to other people about it. A good trick is one that forces the other person to admit they were lying but doesn't cause you to lie/get yourself in trouble to do it. It's not an easy thing to do and usually happens by accident.
I think that these particular examples aren't that rude because if it turns out the person is telling the truth, the only person who looks stupid is you, not them. If you are willing to risk it, that is your business. This is how it could go if they are telling the truth:
A: Oh, you know Alex, isn't he great?
B: Um... she
is great. I have been friends with her
for awhile (Is this employee new or something?)
A: I hate Bob, someone should teach him a lesson!
B: Well he did steal those cookies...
True, they may not actually confess to anything, but there is no reason why they should be confessing to something they didn't do. As to your bolded question, if you explain your plan to Bob, or if you plan this together, there is no reason why he shouldn't believe you.