Hi,
There are snack bars where people can pick up the things that they want to eat and drink, and pay for it at the cashier.
If I want to be polite or if I am not sure that I am allowed to simply pick up an item by myself, can I ask "May I pick one thing here?" and point to the item that I want?
Thanks a lot.
That's very polite!
"Can I have one of those?" is a more likely colloquial question.
You may be meaning to ask "Is this self-serve?" meaning, "Do I help myself to this, or does someone serve it to me?"
Self-serve, self-served or self-service?"Is this self-serve?"
Self-service in the UK, but self-serve is fine.
"Self-serve" is more common in the US.
(Now I know yet another UK/US difference.)