Other uses of the たら conditional

Passing a verb to its past tense conjugation and adding ら makes the sentence a condition, right? Like

暇だったら、遊びに行くよ - If I'm free, I will go to play.

But in the ももたろう tale the たら form is used differently in the sentence:

ある日、 おばあさん が 川 で せんたく を して いたら、
ももがながれて きました

The translation I found states that "one day, WHILE the old lady was at the river doing the laundry a peach came floating by" so my question is: Is this translation any good? Can the たら conditional be used to relate two actions taking place at the same time? Can it be interpreted as 'while'?

Further ahead there's a sentence that says:

ひろって たべたら、
なんとも おいしくて ほっぺた が おちそう。

Which translates as: She picked it up and ate it and, it was so delicious as if to make her cheeks fall.

So what is the role of たら here?

Thank you very much.