How can one tell the difference between plurals in this case?
It it solely based on context?
Most words will have their indefinite article in singular, but not in the indefinite plural. But in many cases, it's contextual, yeah.
It's like fish and fish in English (swedish). The context of the sentence tells you.
Are child and children the same word? Barn?
Yes, most ett-words have the same form in indefinite singular and plural.
Isn't it supposed to be "En barn" since it says "One barn"? It doesn't really talk about "A baby"
When used for counting, we almost always use ett instead of en.
Aren't the numbers always used for counting? Is 'ett' then used for counting also en-words? Is 'one' then ever 'en'?
If you're explicit, you need to use the correct gender, as in en stol. But if you're counting chairs and just go "one... two... three...", you're much more likely to use ett.
Doesnt "man" aslo mean 1?
Yes, but it's in the sense of the general "you" - that is, "one should not drink chlorine", for instance. It can't mean one in the sense of counting.