It could be either. Duo's sentence means "Adults (in general) are responsable"; with the, it means that some specific ("the") adults are responsible.
That is a very good question. I have yet to see any really good answer to this other than the rather vague 'context'. Which doesn't really help us here.
You could differentiate by adding "los" before adultos to indicate you're talking about specific adults and not just adults in general.
No it didn't. It didn't sound like adultos fast or slow. I had to guess.
Spot on Livione97, and watching politicians' antics is the surest way to verify that!
Just to add something I hope is useful: when any consonant (and especially vowels) precede the letter r, it is very helpful in for me to make the sound of that letter as abrupt as possible. Also going through the vowel sounds with a difficult to pronounce word often magically improves my pronunciation.