Naturally the press showed a great interest in her and her family

Naturally the press showed a great interest in her and her family, invariably asking her how she had managed to be elected at such a young age.
Could some please explain the bold part to me?

If you “manage to do something”, it means you find some way to achieve that thing, or make that thing happen.

In this case the thing that happened is that she was elected (i.e. appointed to some position by virtue of winning a vote).

Naturally the press showed a great interest in her and her family, invariably asking her how she had managed to be elected at such a young age.Her answer never altered.[color=red]She owed it all to the way she had been brought up by her mother, Mary. Her father had died of a heart attack when she was only two after his business had been brought down following a financial scandal.

What are the meaning of the bold part and red part?

she had managed to be elected at such a young age.
she had managed to elect at such a young age.
Are the sentences correct?
What is the difference in meaning between them?

Her answer never altered = she always gave the same answer.
She owed it all to the way she had been brought up = She said that she had been elected because the way her mother had raised her had ensured that she had the necessary qualities that the electors were looking for,

She had managed to be elected… - she was the person who was elected.
She had managed to elect… - she was electing someone else. It does not make sense in this scenario.

Is there any alternative that can replace the bold part?

What does “invariably” means?

invariably - without variation.