No. There is no pre-requisite for Psychology. The same goes for Psychology at university. You do not have to have studied Psychology at school level to apply to a Psychology course at University, although of course it would help. Another subject that may be helpful to you if you intend on studying Psychology at University is Biology.
Yes. Psychology is considered a science and as such you will have to conduct various social experiments throughout the two years, including one long experimental study which is your major assessment for Psychology at IB and involves writing a 2000 word report. Part of the process of conducting an experiment is that you will have to do some statistical analysis on your results. In addition, the course does have a heavy biology element. See the subject outlines under 'Syllabus.'
With Psychology, your career options are extensive. Because Psychology is such a vast discipline, it is useful and relevant to almost all careers. Learning to understand how and why humans think and behave the way they do us useful in analysing aspects of society from consumer behaviour to football violence.
The range of careers available to persons having studied Psychology are vast and include, among many others, education, social work, therapy, psychometrics, advertising, marketing, neurology, psychiatry, consulting, communications, nursing, research, HR and entrepreneurship.