It's called a T-pose, and in my experience it often happens when there is an error in the animation. From your description it could be that the sim wants to put away the books somewhere they cannot reach or they get interrupted. Look to see if more than one book case, or storage box, is on the lot, since sims put books in them.
But it sounds like it is mod-related, and since you said you have mods I would try to exclude them first.
1. Long ago it was reported as a bug with MCCC for instance. Create a new user folder by renaming your current one. Make a copy of your save and paste it into the new folder. Testplay, if it happens again. If it doesn't, it's likely your mods, and you need to go through them and look for info on the creator's pages. Delete the newly made user folder and rename your original one back to just The Sims 4, to load it again.
2. Yes, but in my experience they are more of the build bug kind, I'm not sure this one is particular to a build.
3. Data can possibly transfer if you switch between saves in Main Menu, always exit the game completely, and then load a new save if you care about them.
4. See nr. 2. 3a. It's a good method that works for some build bugs and odd issues.
5. Mods and cc is often the cause of bugs, especially when they are not compatible with the game or eachother or just have their own bugs. If you are to use mods and cc, you should learn about them.
Edit to add: If you look in the user folder and there is a txt file called lastException, that could contain the last logged errors in game. You can post it here but I don't promise I'll be able to understand it.
