If Orc Raiders (Road to Rivendell) engages Beravor with Steed of the North, forced triggers before the response and forces her to discard the steed, so it cant be used now? Or she can trigger the steed before discarding it?

At no point after the Orc Raiders revealed from the deck player can use events like Hand Upon the Bow or Galadhrim's Greeting to avoid this?

Encounter effects alway do their effect before players actions. That is the rule.

So when the engagement is made (no matter if you engage intentionally the enemy or not) you have to make the forced before the response. No readying effects for beravor this day. There is some response that cancel an action, only them can be done before the resolution of an encounter effect.

Same things for Orc raiders. The when revealed first must be resolved before doing an action.

The Steed would be discarded before you could use its response.

Thanks!