For searching the room, when they all enter, and one of them asks to make a perception check, just ask them all to roll at the same time and if any one of them beats the DC, then the whole group basically know what that player know (unless you have players that likes to withhold information, like that secret stash of treasure he found in the corner of a room). If all of them failed, I wouldn't allow any further roll on perception unless something major happened, since their character firmly believe they saw nothing so why would the character wants to try and search again.
As for listening to doors, I would probably asks for a stealth roll on top of the perception roll. The point of listening to a door is to try and hear of any activity past the door without arousing attention. If they're not trying to be stealthy (low stealth roll), and just slams into the door while trying to listen to it, have that alert what's on the other side and either comes in to take a look, or set up an ambush for when they try and enter and make all future "listen" rolls against this room to autofail.
Also, if the character with the highest perception is always the first to go, but fails the roll, if I were the other characters, I would just trust what that character says. It makes zero logical sense for the character to say, "oh the wood elf ranger that's suppose to have superhuman hearing failed to hear anything? Pfft, let my bulky barbarian that is basically deaf give it a try". But that's just the way I would play, to try and be in character.
I believe in consequences when a check fails, to make checks in general more meaningful. If there are no consequences, then what's stopping the player to just "take a 20". Failed a perception roll on searches? great, you didn't see the trap and hopefully the player will trigger it. Failed a stealth roll on sneaking up to the door? the player have just alerted the other side of their presence and




will hit the fan pretty soon (assuming there are creatures on the other side of that door).