Terror Ballista

You don't choose a target for Terror Ballista's triggered ability when it attacks. If you choose to sacrifice a creature, a second triggered ability triggers and you choose a target for that second ability. Players may respond as normal to this second ability.

Unearth grants haste to the permanent that's returned to the battlefield (even if it's not a creature card). However, neither of the "exile" abilities is granted to that permanent. If that permanent loses all its abilities, it will still be exiled at the beginning of the next end step, and if it would leave the battlefield, it is still exiled instead.

If a permanent returned to the battlefield with unearth would leave the battlefield for any reason, it's exiled instead—unless the spell or ability that's causing the permanent to leave the battlefield is actually trying to exile it! In that case, it succeeds at exiling it. If that spell or ability later returns the card to the battlefield (as Static Net might, for example), the permanent card will return to the battlefield as a new object with no relation to its previous existence. The unearth effects will no longer apply to it.