No, you must be paid for all time worked. You can, however, be disciplined up to and including termination for working unauthorized overtime. If following company policies means you are having to go into overtime, you should ask the company how they want you to deal with it.
And no, they cannot refuse to pay overtime for the first week. They can, however, reduce the number of hours you work in the second week so that your overall pay for the period does not exceed what you would normally be paid.
Ex. For the purpose of easy arithmetic, let's pretend you earn $10 an hour. That would, for a 40 hour week, gross $400 for one week and $800 for a two week pay period. If you work ten hours overtime in the first week, you must be paid 10 hours at $15 for a gross of $550 for the first week. However, if they require that you go home for the week after 25 hours, so that your two week pay still equals $800 gross, that is legal.
What they cannot do is pay you straight time, or no time, for the overtime worked in the first week, no matter how many hours you total for the whole pay period.
Your best option for being paid what is owed depends on what state you are in.
