The definite article A at the beginning makes the given translation, "The birds are not inside" appropriate - there are some definite birds under discussion, and they aren't inside.
"A madarak nem bent" doesn't really work as a sentence. When you're asserting the location of something, you do need van or vannak ... but you can't use "nem vannak" ... so you use nincsenek.
So how would you say "There are no birds inside?" I keep getting these wrong - sometimes I'll translate something as "X are not here" and that's wrong because it should say "there are no X here." And other times it will happen the opposite way, like it did with this sentence just now. What is the rule for when a sentence containing "nincs" or "nincsenek" means one or the other? Thanks!
This shortening typically happens to á and é when they occur in the final syllable of a word ("closed" off by a consonant at the end of the syllable) and you add endings after them.
madár - madarat, madarak, and so on ...
fonál - fonalat, fonalak, ...
kéz - kezet, kezek, kezem, ...
név - nevem, nevet, nevek, ...
And the opposite happens, too - maybe when the final letter is a vowel? E.g., alma -> almák.
Is there a rule about vowel length changes (in either direction) when endings are added? It seems random to me, and, except for a few that I've simply memorized over time, I can never remember whether the vowel in the final syllable changes (for a/á and e/é). I don't remember learning any rule about that.
With almost all endings, a final a or e will become á or é when you add an ending after it, as you say. That is very predictable and dependable. There is one important ending that is an exception to this rule - the -ság / - ség ending, but it doesn't appear in this Duo course. It's used for forming abstract nouns from adjectives, basically.
There are a few dozen words that exhibit the shortening behavior I described in the post above - one- or two-syllable words, with a long vowel in the last syllable shorten it when you form the plural, or accusative, or other endings that would take a linking vowel. I guess it's best just to think of them as exceptional and make a note of them when you come across them, although I think your ear will soon learn to hear when it's likely to happen before long. (To be fair, though: I just thought of the word sál and realized I wasn't sure whether it shortened in the plural or not. So - there's always an element of memorization, I guess.)
Upon some thought I guess it can happen with í and ú as well. Both híd (bridge) and úr ("lord" or "gentleman" or "sir") shorten their vowel in the plural and accusative. But I think these must be very rare.
yes, if you mention multiple abjects/animals/persons, the copula (to be) should indicate that as well, therefore has to be used in the correct 1st/2nd/3rd/sing./pl. form. So your sentence would be: "A madarak nem bent vannak" - "The birds are not inside" (but maybe somehwere else). - so this could be an acceptable solution.
The word "nem" always in from of the negated word, in this case, the location, BUT: you can not use a negated copula in present tense in neither 3rd person singular nor plural.
So instead of saying "nem van" or "nem vannak", you need to use "nincs" and "nincsenek" (sing./pl.)
so 1st person:
"Nem itt vagyok" - I'm not HERE
"Nem vagyok itt" - Here I AM NOT
and in 3rd person:
"Nem itt van" - S/He is not HERE
BUT "Nincs itt" (instead of "nem van itt")- Here she IS NOT -
The second one sounds a bit like Yoda, but I hope you can understand: in the first case, you negate the location (but if you use this, the location is usually mentioned in the context, or it is implied that you'll tell it as well), in the second case you negate the copula (and there is a less chance that you'll reveal your location, or it is not that important).
Other than this little semantical difference (you'll negate the part you want to emphasise), both versions can be used.