Keep it positive. Always try to put a positive slant on your responses to questions. It’s better to give the impression that you’re more motivated by the possibility of new opportunities than by trying to escape a bad situation. In addition, it’s important to avoid bashing your current organization, colleagues or supervisor. An employer is not likely to want to bring on someone who talks negatively about a company.
If you are currently employed, you should be honest about the start date and show professionalism. You should tell them you would have to discuss a transition with your current company to see if they require a two-week notice (or some other timing). If you currently have a critical role, your potential new employer would expect a transition period.
Seemingly random personality-test type questions like these come up in interviews generally because hiring managers want to see how you can think on your feet. There's no wrong answer here, but you'll immediately gain bonus points if your answer helps you share your strengths or personality or connect with the hiring manager. Pro tip: Come up with a stalling tactic to buy yourself some thinking time, such as saying, “Now, that is a great question. I think I would have to say… ”
When they ask “how did you hear about the position?”, the interviewer just wants to know if you’ve taken the time to research the company and if you have a genuine reason for wanting to talk with them. Mention a product, a mission statement on the website, a reputation for talented employees, or whatever else seems applicable to that specific company. Come up with a great reason. Don’t make it seem like they’re just one company among many. Or that you’re sending your resume out to them for no particular reason other than wanting a job.
Being a good team player is expected, too. But what does this really mean? Getting along with everyone? That’s not hard to do if you’re a nice person. Pulling your weight in the office? Again, expected. What have you done, beyond your job description, that saved the team from a disaster or helped them make an impossible deadline? Have you won an award for this?