Learn English – “Not only from […] but also from […]”

Strictly, the idiom requires parallelism. Not is paralleled by but, and only also needs a parallel. It need not be also; it may be too or as well or in addition, anything which will complete the contrast with only:

I identified with Rowan Atkinson not only as an actor but as a person, too.

You may very well hear the also or equivalent dropped in speech. This is not a casual use, but a (venial) mistake which occurs because in speech we often lose track of our syntax.

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.