For hidden cards that say "Choose a battlefield", like Bone Skewer or Bedeviling Stranger, if I play them from face down, am I forced to choose the battlefield where the card is played?

Yes — when you play either card from face down, the battlefield you choose must be the one the card was hidden at and played from; you don't get to pick a different battlefield.

The mechanism differs slightly. Bedeviling Stranger is a play effect of a permanent, so rule 811.1.d.3 forces its choices onto the battlefield it was played to — and since the "return an enemy unit there" pick must be an enemy unit at that battlefield, the battlefield choice collapses to your own hidden battlefield (FAQ #13084). Bone Skewer is a spell that makes a unit get played, so rule 811.1.d.5 applies directly: if a hidden spell causes you to play a unit, you must choose to play it at the battlefield the spell was played from.

The Tideturner/Evelynn "restricted targeting" escape hatch doesn't rescue you here — that only frees up a unit target that can never be satisfied from the hidden battlefield, not the battlefield selection itself. So at a lone hidden Bone Skewer you can't reach across and force a unit onto a different battlefield; the play is still legal because your own battlefield is always a valid choice.