[discretion22]

Is this company asking you to do things for them by any chance? The only time I've seen anything like this was when they were leeching free consultancy for a problem they were unable to solve. They compartmentalized the problem into different sub-components and under the guise of advancement in the process, held an 'interview' on them separately and a follow-up for the feedback (i.e. find out the answers). Once they had all the parts they needed, they said the person had not got the job.

Find different opportunities - this one sounds no good. If they treat you like this in the play nice phase, they will treat you much, much worse if they ever employ you.