Per the description of Enslave, the Aboleth can use the ability on a creature it can see within 30 feet of it, but its projection lets it see and use telepathy from the new location. I assume it cannot use Enslave since it is not specified, but presumably it is a telepathic effect so I would like to check.
No, it can't.
Though the Aboleth can use telepathy from the projected image, that's referring to the "Telepathy 120ft." communication ability as listed in the languages section of its stat block - so, the Aboleth can telepathically converse at this increased range, and its Probing Telepathy special ability works as normal, since that doesn't specify a range. However, in order to use its magical enslaving ability, the target must be within 30ft of the real Aboleth.
You may want to note that nothing in the description of the Aboleth's Enslave action suggests that telepathy is required to produce the effect - though that would certainly be in keeping with the Aboleth's theme. As written, even a creature which is somehow prevented from sending or receiving telepathic communication is still vulnerable to the Aboleth's enslavement (presuming that whatever effect they are under doesn't also preclude being charmed).