Immediately gift a game

I'm pretty sure the hold is just for trading, so gifting can be done immediatly. You can do it when you buy it or later through your inventory there is a button to gift it.

you can send it, you can do it while you are buying the gift, or store it in your inventory and send it whenever you want

You can gift it during purchase. If you store it in your inventory it has a wait period, but there are ways around that.

Yes. Yes.
As you buy, you can choose to send the gift by email ou steam nickname.
Or you can send it immediately after buying.

Yes to everything. You can gift a game immediately after purchase, it's trading that has a 30 days lock.
You can send it either by email or directly via steam(if that person is in your friend list). Both options are available before you complete your purchase along with the 3rd option of Keeping the game in your inventory to send at a later date. If you choose that then there will be a "Send gift..." option when you select it in your inventory that will give you the previously mentioned options again.