Nouns and determiners
Solution 1:
As a rule of thumb, you can get a so-called "bare noun" when the noun represents a collection of indeterminate items. So for example, consider the pair:
(a) I saw some children playing and some adults going to work.
(b) I saw children playing and adults going to work.
Case (a) uses "some", which you may be used to considering as an 'indeterminate' article. In case (b), no article is used at all.
Now, although "indeterminate", the crucial thing about using 'some' in (a) is that it implies that the children/adults could be specified. In case (b), by using bare nouns, you imply that the children/adults are basically unspecifiable. It would sound a little odd to say, for example:
"??I saw adults going to work. I recognised them as Peter and Jim from next door."
whereas it would sound more natural with the article:
"I saw some adults going to work. I recognised them as..."
Now, this rule of thumb extends to various "set phrases" where it is unusual to specify the particular item in question. For example:
I travelled by plane.
Here you don't generally care about the specific plane. Notice that if you do, re-wording in a way that uses the article becomes more natural:
*I travelled by plane whose flight number was 731.
I travelled on a plane whose flight number was 731.
Solution 2:
No, not always. There is a feature of language known as anarthrousness in which an article is absent where it might be expected. For example, British political parties have annual conferences. When speakers address them, they don’t say, ‘I recommend to the conference . . .’ They say ‘I recommend to conference . . .’ In British courts, barristers are referred to as ‘counsel for the defence’ and ‘counsel for the prosecution’ and not ‘the counsel for the defence’ or ‘the counsel for the prosecution'. Other words which can show this feature include congress, parliament and school.
In one particular instance there is a difference between British and American English. In the UK, patients ‘go (in)to hospital’, whereas in the US, I believe, they 'go to the hospital’. The article can be used before hospital in British English, but only in contexts not involving a patient.