Learn English – Difference between ‘for’ and ‘about’

"One in ten" is a ratio (10%) but does not define the size of the sample or group.

The definition you have for "out of" is correct.

While your phrase "One out of ten people speaks (English) as their mother tongue" is technically OK (though it should be speaks since "one" is singular), it makes no sense because we know more than 10 people speak English. You would need to add a qualifier, such as:

"One out of ten people in my office speaks (English) as their mother tongue".

It implies there are only 10 people in your office.

It's basically the same as your other question and its answer.

In all your examples here, at indicates an instantaneous event (not related to anything leading up to that event) had an effect; from indicates that the effect stemmed from an existing or long-standing condition.

I became hungry at the smell of the cookies.
The smell of the cookies reached you and you became hungry (instantaneous).

I was exhausted from working all day.
Working all day is a long-standing condition, not instantaneous.

I got excited at the sight of her face.
You saw her face and in an instant became excited.

The last one is more interesting:

I'm broke from having spent all my money at the bar.

Although you could have spent all your money in one transaction, so that you instantaneously became penniless, the use of the continuous having spent means that the state of penury has continued since that time. Consequently you use from.

You could even make a more ambiguous case with

I'm broke from all the expenditure I incurred.

But the same analysis applies: you incurred all the expenditure, and an hour later you had still incurred all that expenditure. It's not the same as suddenly seeing someone or smelling cookies.