Question

yes

You can gift games from the UK if the game isn’t region‑locked and the UK price is close to the recipient’s region price as tax is tied to region.
You can’t gift games from the UK if the game has region restrictions or the UK price is too much cheaper, because Steam blocks cross‑region gifts when the price gap is big.

Would US to EU work?

Any region can gift to any region, usually. Sometimes it won’t work, there’s no way to know without trying. It depends on the specific game and the current prices in each region

Can, doesn't always mean it will, you can always get a seller to your ISO and get them to try, can't hurt for them to try...usually a seller who sells a lot of games knows where their region locks against.

If its on sale most of the time no, I did find that out

Seems Forza didn’t work us->eu it’s 70$ there and 70€ here for context