Do CROs go through the same exact trainings as PJs?
No, they are not paramedic certified. Also a PJ you are expected to be proficient in many aspects, such as extrication, ropes, and over all Technical Rescue Specialist. CROs are not necessarily expected to know every detail like a PJ should, they should just be aware enough to recognized safe and unsafe conditions. A CROs main focus is the up and out aspect.
Are you allowing guys to rest during push ups with their butt up in the air or is it starting position only?
Practice without resting with your butt in the air. Know that the rules can change at any time, so be prepared.
For the 500m PAST swim are we allowed to do a combat side stroke or only freestyle?
You are allowed to do any stroke you want. But it is highly recommended you use free style.