Private variables help prevent people from depending on certain parts of your code. For example, say you want to implement some data structure. You want users of your data structure to not care how you implemented it, but rather just use the implementation through your well defined interface. The reason is that if no one is depending on your implementation, you can change it whenever you want. For example, you can change the back-end implementation to improve performance. Any other developers who depended on your implementations will break, while the interface users will be fine. Having the flexibility to change implementations without effecting the class users is a huge benefit that using private variables (and more broadly, encapsulation) gives you.

So this sort of answers question 2. All your implementation details should be private, and the public part should be a small, concise, well-defined interface for using your class.

Private variables help prevent people from depending on certain parts of your code. For example, say you want to implement some data structure. You want users of your data structure to not care how you implemented it, but rather just use the implementation through your well defined interface. The reason is that if no one is depending on your implementation, you can change it whenever you want. For example, you can change the back-end implementation to improve performance. Any other developers who depended on your implementations will break, while the interface users will be fine. Having the flexibility to change implementations without effecting the class users is a huge benefit that using private variables (and more broadly, encapsulation) gives you.

Also, it's not really a "trust crisis". If you make a piece of data public, you cannot ensure that no one is depending on it. It's often very convenient to depend on some implementation-specific variable, instead of going through the public interface, especially in the heat of a deadline. Further, developers won't always realize that they are depending on something that might change.

So this sort of answers your other questions, I hope. All your implementation details should be private, and the public part should be a small, concise, well-defined interface for using your class.