How much knowledge is expected of an MPhil applicant as compared to a PhD student, a postdoc or a research assistant?
How much is expected of background knowledge for an MPhil applicant? 


This depends a lot on the domain and the institution, and MPhil doesn't exist in every country. So it's impossible to answer this question precisely, but I think one can broadly define the differences in terms of how operational the person is expected to be at producing research:


A postdoc is a professional researcher hired on a temporary basis. For all intents and purposes they must be able to carry out their research work on their own (i.e. produce research), under the direction of a PI.
A PhD student is training to become a researcher, and this training includes producing research. They are not expected to be autonomous in the production of research, their PhD advisor is here to train them. However they are supposed to have acquired the background knowledge and to be able to complete their knowledge in their specialized field on their own.
An MPhil student is at the initial stage of research training. They are expected to require more supervision and are not necessarily required to publish papers.
A research assistant is simply somebody hired to assist in research. They are not expected to produce research by themselves and might have a very limited knowledge of the research questions. For instance a software developer can be hired as research assistant in a physics project where they provide a service according to their skills. In general this is not a training position.