Maybe it's age related, but if any of the scenarios you wrote happened to me, I would not be embarrassed receiving someone's assistance.

Coming up with the right phrase in the moment sounds risky. Is there another phrase you can use to offer help ?

> If you just shout "hey you need help?" ...

There's also another more neutral option. Just give them the answer they need without the fluff. If they then want to thank you and chat it's their choice, but completely optional.

This is probably not the right approach most of the time, but it works well on the types of people who seem "serious" (not anxious or upset).

This is a really hard one to pull off. You have to determine that they really are that type of person and then just magically know what they want. It's really satisfying when it works though.

I've met some of the most interesting people I've ever known that way.