Illegally obtained evidence may still be used in court in Victoria, but only where it is compelling and vital evidence, and where the greater benefit to society is found in conviction of this specific offender for this specific offence rather than in upholding the ethical standards found in evidential law.
Also, to make a report to Centrelink one usually does so through the fraud line that covers Centrelink, Child Support and Medicare fraud. Thought it is unlikely that they will charge an individual for making a false report, they may have the power to do so where is it apparent that the report was made vexatiously or to obtain property via deception.
In addition, Centrelink might commence an investigation. Should you have all receipts for your rental payments you should be fine. In order for him to show that he paid rent and lived there, he would need to show evidence or direct payments made to your landlord (receipts) or to you (receipts and statements). He could he withdrew the same amount each month on the same day of the month. He might then subpoena your bank records to show that the balance of the rent due was withdrawn from your account rather than the entire amount.
If you have nothing to hide then let them report what ever they wish. You can comfort yourself with the thought thtat they are wasting their time. You are not obliged to return gifts under any circumstances, and the phone was provided as a replacement to pay for damages incurred.
If the ex was violent or abusive, and this includes verbal, financial and physical abuse, and you feel that his actions are threatening, you may apply for an intervention order through the Federal Magistrates Court in Melbourne and its equivalent in other jurisdictions. This can act to prevent both him and any person acting on his behalf, from making threats or demands, and from harassing you.
As I am a student of Law, I recommend you seek advice from a lawyer (legal aid or community legal centre). A lawyer may contact the regulating authority that the Ex's family must register with to obtain a licence to practise. Their licence may be revoked.