Last Caress

Yes, Last Caress lets you play the next unit this turn to a battlefield where you control no units, as long as you could otherwise play it at that time and no restriction or mandatory requirement limits its location.^{355.17355.17.b} Last Caress independently makes every battlefield valid for that unit, even when [Ambush]'s own location permission does not apply.^{355.2.b822.3.a}

This changes only where you may play the unit, not when. Last Caress does not grant [Reaction], and [Ambush] grants [Reaction] only while you are playing the unit to a battlefield where you control units.^822.1.b813.4

No, if Here to Help was played from face down, Last Caress does not let you play the unit from your hand at a different battlefield. Once you choose to play a unit, Here to Help's "to a battlefield you control" instruction is a mandatory requirement on its location.^355.17 Because Here to Help was played from face down, the facedown rules also require that unit to be played at the same battlefield.^811.1.d.5 These requirements do not conflict and must both be followed.^355.17.a Last Caress makes additional battlefields valid locations, but it does not remove either requirement.^355.2.b Any different battlefield fails the facedown requirement, and a battlefield you do not control also fails Here to Help's own requirement.

Last Caress's "even from face down" text applies when the next unit itself is played from face down. Here to Help instead instructs you to play the unit from your hand, so that text does not override the requirements imposed by Here to Help and the facedown rules.