I would separate them as early as possible. When they grow bigger their branches will rub against each other and can get easily broken.

It is possible to do but will require a lot of pruning to keep small, really more like fruit bushes than trees. Starting from a seed from an apple as you have, you will have no advantage of a dwarfing rootstock, and the resulting tree will be a vigorous grower attempting to reach 30 feet. You should also not expect the resulting fruit to resemble the apple the seed came from. And it could take up to 10 years to get fruit. Al

Oh yes I know about the not true from seed thing. Thanks guys for your insight.

Depends on what effect you are looking for. There are plenty of examples of groups, circles, pairs of trees which have grown up together and look very good. I was just looking at a group of 200 year old beeches in my local park, 5 I think, which stand in a circle and form one giant crown. But it may depend on your climate and whether you are prone to snow load, high winds etc.

Not my own picture but this is the group I mean.

Here is a link that might be useful: Group of beeches

Here in the Redwood Empire of California, when the original redwood is harvested, usually leaving a stump with a diameter of 4 to 8 feet, three to five new trees will grow around the edges. If a grove was originally dense, the second growth will be even more so. In the case of fruit trees, the tree must be kept open to sunlight or the amount of fruit, will be limited. Al

Neat to know Al.

You could investigate espalier/arborsculpture techniques to help you guide these trees so they grow to your liking and desired shape, not just willy-nilly in whatever way they want.

Apple is known for its' ability to inosculate, so as the trunks expand, they will likely fuse together and appear as a single tree/trunk.

Here is a link that might be useful: Wiki article on inosculation

It is a bad idea, as with Crape Myrtles they will rub together and they could possibly break.

I agree with separating them asap. Doing so will let them both grow without competing for nutrients and space. Separation will also help if either of them has any ailments.