Everyone should check out duolingo on their computer so they can see the tips for each section where most of this stuff is explained. This is the major shortcoming of the app.
Is there a way of telling between "She has children" or "She has child" (without article)
You wouldn't ever say "she has child," it just doesn't sound right in Swedish. They would always say "she has a child," they never leave the article out in that sort of sentence, especially considering leaving it out changes it from singular to plural :)
Not really, this can mean that she has either one child or multiple children, to clarify you’d add a numeral or say ”many” or something similar.
I saw someone post before about "ett barn, barnet, barn, barnen" - is barnen just another way of saying pleural barn?
From what I can tell - barnen is the pleural with "the" added, i.e. "the children"
ett barn = a child;
barnet = the child;
barn = children;
barnen = the children
Yes, this is the general rule for "ett-" words ending with a consonant (such as ett brev, ett barn, ett problem, ett hus): -> plural, indefinite form: the word does not change: --- brev = letters --- barn = children --- problem = problems --- hus = houses -> plural, definite form: you add "-en" in the end: --- breven = the letters --- barnen = the children --- husen = the houses