Depends entirely on whether the outcome is in doubt. If the guards are drunk, then stealthing past them may require no check at all. In other words, an auto-success. If the lock is very simple, and the one picking it very experienced at picking locks, then asking for a roll may be a waste of everyone's time.
No. But I think it is a little bit silly to have the players roll perception checks to spot their friend in a crowd, when narratively it may be in the best interest of the story for them to meet up. This is of course assuming a situation where neither person is trying to deliberately hide from the other. Sometimes rolls can get in the way of the flow of the game. In such cases I lean more towards no-roll.
You phrase it in a perhaps overly complicated way, so allow me to try and rephrase it a bit more clearly for anyone else reading this.
Whether a character 'knows' some bit of knowledge is determined by a few factors in my campaigns:
-Is it common knowledge?
-Would the player's character be likely to possess the knowledge, given his class and backstory?
-The stated approach of the player.
If I am in any doubt whether the player knows the information given the above rules, I may ask for a roll AFTER the player has stated an action. If the resolution is not in doubt however, I may hand the information to my players immediately, with no roll required.
This means that any player would recognize the statue of the king, but the cleric may be the only one who recognizes a statue of a saint. Since it would be in doubt whether the other party members recognize the saint, they would need to make a check after asking me (their DM) if they know the saint. This of course also goes for any other rephrasing of the same question. Basically, if they decide to investigate, or ask me for information, that is when I decide if the outcome is unclear.
A stated approach could be: "Does the statue have a plaque? If so, I read the name underneath the statue." If the name is on a plaque underneath the statue, then there is no chance for failure, and no roll is needed. There is no need for me to hide the info behind a die roll if this is the case.
I believe this is better than having everyone who enters the room immediately make a perception or knowledge check to identify the statue. Because what would be the outcome of failure here? One or two people fail their checks and their characters don't know who the statue is? But if someone succeeded at their check, then basically everyone at the table now knows the outcome, regardless of what their characters know, and you've basically forced half the table to roll for no good reason. If you instead wait for someone to take an action to investigate the statue, you cut a lot of time wasted on meaningless rolls, and focus instead on what the players choose to have their characters do. A lot of DM's seem to use this auto-roll style as a sort of clumpsy trick for getting 'someone' in the party to obtain some bit of expository information. But if that is the case, just hand your players the information right away. Why beat around the bush?