Your translations are correct. In particular, in Italian the indefinite article can never have plural meaning (although it can have collective meaning), as in English. Sometimes you can use the partitive article ("dei"), but it is not very common.
I have no systematic knowledge of when you use the articles in the two languages, but I would say that regarding the usage of the indefinite article they are quite similar. Incidentally the sentence I have just written provides a counterexample:
I have no systematic knowledge of ...
Non ho una conoscenza sistematica di ...
On the other hand
I go running once a week
Vado a correre una volta alla settimana
Here the indefinite article becomes preposition + definite article.
However, differently from the first example which is applicable to more or less every negative sentence, the second example seems to me more specific, tied to a particular idiomatic construction in English.
So, I would say that the usage of indefinite articles is mostly similar, except in negative sentences like mine above where the English particle "no" stands in the position of an indefinite article. Since Italian has no way to produce a negation just by changing an article or pronoun (you always have to negate the verb itself with "non"), the English "no" particle has to be traslated with an entirely negative sentence; so the "no" particle itself can become an ordinary indefinite article (it could also become "alcuno" or "nessuno", which are more properly translations for "any" and would stress even more the negation in Italian). Then there are many other situations where the usage of the definite or indefinite article (or no article at all) depends on a specific idiom.
Let me just mention an occurrence which I find funny: the three expressions "il giovedì", "un giovedì", "giovedì" roughly translate to English as "(usually) every Thursday", "one of the next Thursdays (when we have time, probably)" and "next Thursday".
For the definite article the issue is more involved. Again, I have no systematic knowledge, but my general feeling is that English tends to use it a bit less. For example it does not use it in front of uncountable nouns and plural nouns with a specification:
Little children are pretty
which in Italian is
I bambini piccoli sono carini
However the matter is much more complicated and is not the subject of your question.