"Det är ert barn."

Ja. If it were children, Det är era barn.

Yes, it's all clear to a native. Furthermore, the vowels are different; short in ett, long in ert.

It rightly wasn't; it's silent.

I'm a native, and I'd say that while native Swedish is often as fast as TTS here, the TTS seems to be a bit too sloppy here.

I am not a native speake of Swedish, and I would say that I usually find Swedish to be more clear than this. The vowels themselves are ok, but I think the voice could have more stress between words. That is, not deeertbarn but more like de'e'ert'barn.

The difference is in number, singular or plural.

Din/ditt/dina goes with du/dig, the singular second person pronoun.

Er/ert/era belongs to ni/er, the plural second person pronoun.

You tell from the pronoun. ert barn = 'your child'. era barn = 'your children'.

This is your child would be either Det här är ditt/ert barn or Detta är ditt/ert barn. There is no difference in meaning between den här/det här and denna/detta, but when used with a noun, they function differently grammatically: we say det här barnet but detta barn.

I think you have to memorize them, here is a good site ! :)

http://www.systranet.com/translate/

One thing I've found that really helps me with this is to try to learn the word in the definite form, rather than in the indefinite form. For example: flicka (girl) - I learn it as 'flickan' (the girl) ... or ... hus (house) - I learn it as 'huset' (the house)

That helps me to get the gender and endings thoroughly attached to the word.

I add words to my own list whenever I hear new ones.

Er is for common gender nouns ("en" words), ert is for neutral gender nouns ("ett" words).

In Swedish, like in many languages, the word for Child is gender neutral (it) (so one child = ett barn).

Ert = your (second person plural, as if you're talking to perhaps a man and a wife together), ett = a(n).

No, since "ditt" is used for a singular ett-word, that would mean "it is your child".

It is an informal way to say 'ert'

Er = common gender nouns, ert = neuter gender nounds, era = plural.

Child is neutral (ett) so you you "ert" instead of "er" (you'd use "er" for son or daughter specifically, for example).

Du is singular you, Ni is plural you. In that respect, imagine that you'd say Din when talking to the mom, but Er when talking to the mom and dad together.

Barn is a neuter gender word (det barn; barnet) so it takes a neuter gender adjective ending

We usually pronounce it very weakly, basically we normally just say 'det är' as 'dee' (Swedish pronunciation, not English!) with a slightly prolonged e-sound.

You can say Hon är ditt barn or Han är ditt barn, but that's not what the sentence means – det does not refer to the child, it's a placeholder pronoun. See this thread for a longer explanation: https://www.duolingo.com/comment/9708920

For a short fix, consider what you'd say if there was a knock on the door. You can't see the person and someone asks you who you think it is. You wouldn't say 'She's your child' but you could say 'It's your child'. (more likely of course, It's your daughter, but still not She's your daughter)

Although barn is an ett word, we actually normally don't use det as a pronoun about children. So no, it doesn't work like that.

This is fairly common in languages, I think. Presumably it's to avoid gender confusion when identifying a child - historically Swedish also had three genders, though the masculine and feminine disappeared. I assume this is a holdover from the earlier language though.

'ditt' for something that belongs to one person, 'ert' if it belongs to more than one person

Think of "ditt" as being used in a conversation with one parent and "ert" as being used in a conversation with both parents. In English we only have one "you", but most European languages have a singular you (for talking to one person) and a plural you (when talking to an audience of multiple people).

This has been discussed a bit already in this conversation chain - please read other comments in the future, you might find your answer there.

See e.g. reply by keinemeinung on this page.

"Ert" might be used because the owners of the child are more than one (you maybe talk to a couple and ask them if the child is theirs). It could also be that you use the polite and slightly old fashion "ni" instead of the normal "du" when you talk to a single person. But if you are talking to a single person, you can use "ditt".

See my comment above

Plural - the singular would be ditt.

I think it would sound better to say "They are your children", no?

The "t" at the end of "er" gives it away - "er" would be for common gender, "ert" for neuter, and "era" for plural. So it can not be children.

No, they are is plural, child is singular