No Longer Able to Save Steam Gifts for Later?

As far as I know, yes. You don’t need to have it on hand when you start, you just have to keep your promise to deliver the game. I would suggest leaving ample time for yourself/ noting in the description that this is what you’re doing to increase the chance that the winner acts faster. Which isn’t a guarantee either.

Basically yes but u cant gift to other regions by some werid rules that i dont know detailed, since Store disabled saving gifts and cross region gifting i left Store

Yes, it is. Just be aware that you can't send a game via Steam if the price difference between your currency and theirs is higher than 10%.

I usually recommend restricting to your own country when doing these kind of giveaways to avoid issues with delivery.

that's fine.
take into account that there might be a delay after the giveaway ends (winner has 7 days to accept your invite/gift). if you plan on buying games with discounts, you could miss them.