Hi
@Riaz,
There is an article on here that explains criminal background checks and will answer you question on spent convictions:
What Would A Police Check Reveal About You? - Blogs - LawAnswers.com.au.
As for purchasing car/home insurance, you are not prevent from applying for insurance at law. You can apply at any time. You may face difficulties with the insurance company, who may request a criminal background check and raise your premiums because of your past conviction (as you may be seen as a riskier applicant). However, you will unlikely be denied insurance and most cases, I don't believe there will be an issue until you make a claim (you may be investigated more rigorously).
This really depends on the private arrangement between you and the insurance company. If you want more information, you could try contacting the
Financial Ombudsman Services to enquire about what factors insurance companies are, and are not, allowed to take into account when setting rates for premiums.