does this mean, in italian, the same as it means in english? (ie, she is not the one who is responsible for a thing, but also, she is not a responsible person.)
Yeah, it can mean both. There's no distinction as it happens instead in German, for instance, which has zustandig and verantwortlich.
This has a peculiar sound when it pronounces the R, I've heard people actually pronouncing it like that, is it normal?
Not sure if you mean the rolled R (similar in Spanish) which sounds almost a bit like an L? We don't use it in English.
I wrote this comment when the course had a different TTS, the current one pronounces it correctly. Instead of rolling the R properly it sounded like the mixture of an English R and a Spanish R.