You can graft seedling onto an established tree, assuming you have reason to do so. Usually the big benefit of grafting is that you can take a variety of known good characteristics and get an exact genetic duplicate growing on another rootstock. More often seedlings would be used for the rootstock, rather than for the tree.

Persimmon and apple are not compatible. Grafting persimmon onto apple will not work. I think just grafting persimmon to persimmon isn't the easiest although I don't have a lot of experience.

I've heard of people having success grafting pear and other pomme fruit to hawthorne. I have a hawthorne serving as rootstock for what I hope to be an Asian pear eventually. I have an Old Home pear serving as an interstock and I've budded Hosui onto the Old Home. If those buds don't take I'll try a whip and tongue graft this spring.

I've heard of other combinations of interstem to get apples and probably quince onto hawthorne.

Your best chances at graft compatibility is to keep to one species, apple to apple, pear to pear, etc, although it is no guarantee and there are plenty of cases where certain specimens of closely related species are graft compatible.

Persimmon and apple aren't that closely related.