If you otherwise qualify for pps (income limits, age of youngest child etx) there is no reason you couldn't apply for it.

Call up and speak to the carers team. Regarding hours worked and respite etc. Given your child I you receive carers for will be in school., I'm not sure how repute works exactly - but there are a certain number of weeks you can go over the hours worked without losing carers by accessing respite provisions. The carers team would be the only ones to give you a clear answer.

If ou remain on carers or pps, nothing would change with ftb. If you go off income support your ftb will be based on your income estimate. Your child support may be impacted either way. You would need to speak to child support to discuss that one