Translation:Were you born in the twentieth century?
It's a question of a result that still remains or not. Like, Dörren är stängd 'The door is closed' – the result of the action of closing it still remains. Dörren var stängd 'The door was closed' – either this is a part of a narrative wholly in the past, or the door is no longer closed, i.e. the result of the closing action no longer remains.
I understand what you mean, and it may just be due to the analogy you gave, but a door can be 'unclosed' I.e opened again, however a person cannot be 'unborn' I.e go back into the womb (unless you're in a very odd family), I'd equate being born more to a cake being baked, or some kind of food that has been cooked, since you can't uncook food. It's an irreversible process. Like being born, either its happened or it hasn't. And you can't go back to gestating.
You're right that a cake would be a much better example. It would work the same: the cake we ate yesterday var bakad by my dad but the cake we're having now är bakad by my mom, and we can't say that the cake which is on the table right now var bakad by anyone. Because it still är bakad – the result remains. When we have finished the cake, the result of the action is no longer at hand in the present, so the verb changes to the past. – Whereas the English language thinks as you outlined: once it has happened, it has happened. And obviously the baking took place in the past, so it's fine to say that the cake on my plate 'was' baked by someone. But from a Swedish point of view, that would be much like saying that the cake 'was', say, 'round' regardless of whether it still exists or not.
This difference makes the passive sort of difficult to teach via translations, because the languages don't correspond that well.
There are many ways of thinking about this. I'm not trying to say that anything is more or less logical per se, it's more that trying to see this kind of pattern can help you remember how it works. One way of thinking of it could be that the Swedish participles are really much more adjective-like than their English counterparts. Which can also explain why we use them much less and in more restricted ways.
So is that the reason why Swedish doesn't have immediate present tense verbs like 'going' 'walking' 'studying' etc with the 'ing' suffix to differentiate from doing something in general as opposed to doing it at this exact moment? Because I think I'd have trouble explaining myself in Swedish to a swede without having to resort back to English, if I said 'i study' in English that would mean that in my pass time I do a bit of studying, but to a swede that would seem to imply that I've got my books and revision notes out right now. How do swedes differentiate between immediate and general present tense verbs? Or does that differentiation not exist?
Maybe it's too much to say it's the reason, but at least it must be part of the reason. You can say Han är döende 'He is dying' but then the participle döende functions like an adjective, it describes a state or characteristic, but not a verb action. You cannot say Han är läsande where 'reading' in 'He is reading' is very active.
There are also nouns ending in -ande so that you can say Han är studerande but it doesn't mean 'He is studying', only 'He is a student'.
PS: link to a thread about how we 'cope without the immediate present tense': https://www.duolingo.com/comment/5954508
Another interpretation of the case with the cake is that the verb vara in Swedish is very much more sensitive to changes of state than be is in English. There cannot be a change of state together with vara, because then we will use the verb bli instead. Whereas there's much more overlap between 'be' and 'become' in English.
E.g. in English you can say that She wants to be a doctor to mean the same as She wants to become a doctor but in Swedish you really have to use bli for this sentence for it to mean what people normally want it to mean.
Of course in the sentence kakan är/var bakad there has been a change of state from unbaked to baked, but that change took place before the time frame of the sentence and only remains as a result.