[RPG] Does reapplying Hex cost a spell slot

No, you can't

You have answered your own question. I understand what you say by RAI could possibly support a "YES", but the RAW clearly does not. You choose how you want the hex to work when you cast it.

Also, Choose one ability when you cast the spell.

The bonus action to move it to a new creature simply moves the hex and doesn't allow or state that you can alter the terms of your Hex.

Yes, a warlock can keep the hex spell up outside of combat.

In-game, a turn is defined to have a duration of 6 seconds. When not in combat, you are not in initiative order, so turns are not structured rigorously. Nevertheless, your "turn" out of combat occurs whenever you have the opportunity to do something. As long as you have 6 seconds to spare, you can use your bonus action, and therefore you can redirect your hex.

As you noted, this is also implied by the extremely long durations that Hex can have. Nobody will ever be in a combat that lasts 8 hours (that's 4,800 turns!), so the only reason for the duration to be that long is to allow it to be maintained across multiple combats (or applicable social encounters) throughout an extended period. This is also mitigated by the Warlock's spell economy: they have very few slots to spend, so the requirement to spend a slot on Hex mitigates what could be perceived as an overpowering effect.