In defense of some of these: Doors. Sometimes you are coming up with creative ways to open doors from a distance, a round doorknob is common today, but not as much so in the past, a with a twisting bar is much easier to rig up with a rope to open from 50 ft away, similarly, if the hinges are on this side, then its much easier to just take the whole door off the frame if its locked.
Asking permission to SKILL: Some dm's are more restrictive when rolling, and most dms get annoyed when players just throw a d20 and start saying I want to do a .... 4 Investigation check on my friends armor ....20 intimidation check. Even if you are saying I am going to Intimidate The goblin, maybe it just auto succeeds, no roll needed.
Permission to Insight: Ironically this is reprimanded in this very same thread. Some DMs hate PCs trying to get gut feelings on random NPCs, some DMs hate PC asking permission to use the skill. Lots of people seem normal at the surface level, but you still get a gut feeling that there's more than meets the eye. Personally I think the DM should roll insight behind the screen and tell the player the resulting insight gained. Maybe a 3 the DM will tell the player that you can see him doing small ticks while he is talking, and he is probably dishonest. Insight isn't an automatic lie detector, but it can give you just a hint of someone's mindset or what is going on. Maybe this person giving you the details seems like he is hiding great sadness, or is anxious, or excited. These give some Insight to a character without flat out saying "He's lying and secretly parading around town with a bigfoot costume to draw attention to the town"
Does [Character] believe/know X? Again, this is sometimes a valid question that a player may ask to try to role play the character correctly. Does the character know that there are neutral undead revenants? Do they know that some effect they witnessed could be created by a low level wizard. Do they know some information you gave to another party member but hasn't explicitly been relayed to this character? I personally asked as I saw a party member down, I moved to save them but didn't use action surge because the character had no way of knowing she was already 2 death saves in. As a player I would have burnt everything to run up and stabilize, but my character had no idea her condition was so critical (he was able to wait 2 turns to save her literally a few turns prior)