If you do in fact have a rootstock tree then you shouldn't have any problem grafting onto it. Just find varities that you like and use them for graftwood. Leave at least one strong branch with plenty of foliage to feed the tree.

Sounds like you do have a plant that is a rootstock-- does it have a lot of thorns on it?? a lot of rootstock varieties do-but not all.

You don't need to leave a branch on, witch is called a "nurse branch" since its probably planted in the ground I assume, that is used mostly but not exclusively for container stock.

Grafting is an acquired skill that takes a small bit of learning, best done by hands on experience learning from a person who is already accomplished in the skill especially on mature in ground trees, you can learn on your own by watching grafting tutorials on other web sites and starting on small seedlings or branches of the mature tree. Its not rocket science-- but to be successful you better know what you are doing before you whack down a 20 year old mature tree

yes you can graft onto old trees. The readers digest version is:
make sure you have your grating stock on order or picked out so you will have it at the right time. Plan to graft several branches for each tree.
Cut back the old tree with a hard pruning to stimulate lots of new growth. Be sure to paint all the bark with white latex within one hour of pruning to prevent sun burn of bark.
In 4 to 8 weeks you should have vigorous new shoots of tender green growth that you can graft too.
Remove all branches that are not being grafted.
good luck