An example of a tough introspective question must be the classic "what's your greatest weakness?". Behavioural style questions can also be tough to answer: "tell me about the worst coworker you've ever had and how you dealt with him or her". There must be a by-the-book way of assessing these types of questions or they wouldn't be so frequent. What is that way?
I don't think these questions are tough. They are tough if you are obsessing about ways to spin the answers to make yourself look good.
If you answer these questions in a way that shows the real you, the answers will be nuanced,more realistic and give the interviewer a level of comfort about what you are as a potential team member and coworker - Yes, managers are team members and coworkers, too. And it can turn out that they have less latitude in making a range of decisions than their subordinates.
My greatest weakness is also my greatest strength. My greatest strength is that I don't know when to quit, and I have orchestrated many a turnaround that way. On the other hand, there is a lot of value in quitting and stop throwing resources that could better be allocated elsewhere, and since I am not really well wired to quit, I have to manage that weakness 7x24.
One of the worst coworkers I ever had was a junior who was working for another senior. He asked for my assistance 24 hours before the report was due and just after I had spent the previous 24 hours with no sleep, handing my own reports to the clients on time. I was utterly exhausted when I looked at the kid''s report at 4 PM and I realized that a total piece of garbage that had to be rewritten from top to bottom. To add insult to injury, I had expressly told him two weeks earlier not to wait until the last minute before asking for help.
We finished the report between 4 PM and 4AM the next day and throughout the night, I tore into the kid for his begging for help at the last minute when I had expressly told him not to wait until the last minute. As for the senior, he had bailed out and quit the firm the week before.
I am certainly not coming out of these stories looking like a saint or the epitome of perfection, but those employers who hired me weren't looking for one. And most likely, they didn't want one. Because they had real problems to solve and real issues to manage.
Try to come up with your own, real answers - The interviewers can spot canned answers coming at them from the horizon.
I don't know if there's a "by the book" answer. Interviews, by their very nature are a bit scattershot and biased towards the... biases of the people asking the questions.
Personally, when I ask these sorts of questions, it's because I think you can't be critical or honest. I dislike canned answers. I dislike "I don't have any weaknesses" or "my greatest weakness is sometimes my awesomeness makes people uncomfortable" - everyone has weaknesses. In short, I want to hear you own something bad about you, or the fact that a bad coworker was just bad. I don't want to work with someone who is too scared to give me bad news, or ignorant of their own flaws, or who pushes their mistakes on to others.
Other people I've known want to see how well you tell a story. How can you take the bad coworker and tell a story that puts you in a good light - since you'll often need to tell a good story to customers/managers when things don't go smoothly.
Others still want to see what you consider a weakness or a bad coworker. If you spell out traits that mirror things they value as strengths... you'll probably not get the job.
In short - it depends. The fact that these questions are common doesn't mean they're any good. It means that many interviewers, when thrown into doing an interview think "oh, what common questions should I ask?". Since these questions can apply to everyone, they proliferate.
These are standard questions to get an idea about your personality and your ability to work with other people. Some of these questions are useful and some are not.
IMO, questions about team work and conflicts are okay.If you are a new grad, then you can share your experiences about the college team projects you did. Mention all the conflicts and how you resolved them.
IMHO, the weaknesses part is just a silly question. Who likes to mention their weaknesses unless it can affect their ability to do the job ? Eg. If Billo has frequent seizures and insomnia he cannot be a commercial pilot. On a light note, example of a weakness: I have a weakness for seeing cute cat videos on youtube while working. But this is a strength because it helps me to refresh my mind.
How to get a list of such questions and answers to them ? Search google and or ask your friends who have some years of experience. They will tell you how to play this game. You could also get a book for this.
Here are some links for such Q/A: http://www.businessinsider.com/how-to-answer-greatest-weakness-interview-question-2014-3
Here is a link which has a funny take on such interview questions: http://theoatmeal.com/comics/interview_questions