Here I'm going to break down why (from a game design perspective) why these wouldn't be added. Also sorry for any grammatical errors as I am writing this at 2am after a long day of doing assignments for my game design course.
#1: That is a copy of the jump rope girl and how you get the books. To add a character like that it would have to have unique attribute a possible solution (albeit a bad example) that the nerd character would give you an special item only from him. The questions would be harder than the ones in the book (but all possible) and if you answer one wrong Baldi would increase his speed by 3 and the nerd would only appear after the 4th book. But still this is a bad example as it is very similar to the jump rope girl. Also adding another character would ruin the game. We have sweeper, Baldi, headteacher, girl, bully and the sock. The balance these have at times can be unfair but all the same that makes the game but then another character like this thrown into the mix would ruin the game.
#2: As you realised that it is dumb so I'll keep it short. Your idea renders the calculator useless as if Baldi still gets mad. (As with all programming based ones i will add an example to help it even if it still would be bad from a design sand point but it depends on the devs ideas of it) The calculator would only appear after a certain point (5-6 books) but if the principle see's you with a calculator in you inventory (even if not equipped because of how op it is) and it is a difficult item to get maybe even if you have to have 2 quarters and the tape so you have to choose what you want to stop baldi getting you in detention or the calculator.
#3: This would be difficult to do but not with implementing it. This game has a specific art style set now and it would break the experience of the game. Here lets say a game like GTA 5 or The Witcher 3 changed it's art style to a super cartoony art style that would change the feel and break the game for many people.
#4: Well the flaws with this... The time length is the worst part. (for some players this would be like a dream) 2 minutes is a long time maybe it could be like 5 seconds at most as that way you are not removing the threats for 2 minutes. If in dark souls you could get an item that you turn off the AI for the bosses for 2 minutes it wouldn't be as hard but that is the point of the game. 50% chance of working is way to high for this to work it would have to have 20-25% chance and a cool down as if you spammed it with a 50% chance it might as well have been a 100% chance. Then once it works the item is destroyed. I'm not sure if in your idea it got destroyed or not as you didn't specify. If it was destroyed on 1st use in yours then lets say this does that but if we use my original improvement it would be a very rare item with a 0.1% to spawn. The reason why it is 0.1% because the way I can think of it being programmed it would have multiple spawn locations where it would spawn at a random location so each area it tries to spawn. after it has ran through all of these it has a like a 2-5% chance to spawn