Your Table's Social Contract Is The Key
I strongly recommend bringing all of these points up with your own group of players, out of character, to discuss how they feel them about them. Do your players think they should be able to do things without the other party members knowing? Do they want nothing kept secret from all players, feeling comfortable without play without letting their characters act on knowledge they shouldn't have? Or would they prefer to be kept in the dark of any knowledge their own characters wouldn't know?
And how do they feel about tricks and skills being used against one another? Do your players, again out-of-character, feel comfortable with letting the rogue PC steal from them? Do they want to role-play that out, struggle with those kinds of conflicts in-character? Or would they very much rather not bother and get on the business of adventure and do-gooding? If it's the latter, tell your party rogue in no uncertain terms he's not allowed to steal from the party. Appease the little klepto by giving him plenty of situations to pilfer from the party's mutual enemies, and everyone will be all the happier.
If you're asking for advice on which way to lean, no one can do anything more but share how they handle these situations at their own tables. In my case...
Secret Knowledge is A-OK
I love suspense, and in particular I love to create suspense through dramatic irony, which is when the audience knows something the characters don't. When the audience and characters are one-in-the-same, I create dramatic irony by only revealing crucial information to certain players (and thus, certain characters). What those characters choose to do with that information, and what they choose to share, is ultimately up to them. I once had a character who had detect evil at will, but was generally a moral relativist. I'd reveal that information to him every time a new NPC was encountered, but he never shared it, because he never felt the information to be particularly relevant. This has always worked great for my table.
Game Mechanics are PC vs NPC ONLY
This is a hard and fast rule of my own. I feel very strongly about it, but I also recognize that other players feel very differently. At games I DM, the game mechanics exist to resolve conflicts between the PCs and my NPCs only. PCs do not roll dice to oppose one another. Bluff, Sense Motive, Intimidate... these are skills I reserve from PC/NPC interactions, not PC/PC interactions. I don't even allow attack rolls (including grapples) any more except in extreme circumstances that I've planned for and telegraphed in advance (the party tracking down and facing a powerful Illithid Dominator, for instance). The only real exception I make to this rule are Perception checks; party members should always have a fair chance of perceiving what other party members might be trying to hide from them, but I handle these situations as above in terms of secret knowledge. There are role-playing systems where PVP and inter-party conflict work great; in my opinion Dungeons & Dragons in any of its forms or derivatives are not included in those.
Ultimately, Play The Game You And Your Players Want To Play
This goes back to the idea of the Social Contract. Ask all of your players how they feel about each of these points. Allow them to state their cases, state your own, and attempt to reach a consensus. If there's a disagreement it's up to you to make the final call, which is why it's still worthwhile to hear what other DMs would do in those situations, but again that has to come down to the type of game you'd prefer to run.