I am in Australia, but my children are in my home country living with their grandparents. Can I add them to my partner visa application when I lodge it in Australia?

Unfortunately, you can’t do that. Once your Partner Visa is granted though, you will be able to apply for Subclass 445 Dependent Child Visas for your children. If you have the correct consents or family court orders in place, they will be able to migrate to Australia and be added to your Permanent Partner Visa application (Subclass 801).