It is den vita årstiden instead of den vit årstiden because årstiden is a definite noun. Adjectives for definite nouns, irrespective of gender or number, always get the -a ending (except for naturally masculine words, who get -e). This wasn't explained yet but can be found here: http://en.wikipedia.org/wiki/Swedish_grammar#Adjectives
This is another peculiarity of Swedish - sometimes the definite is formed both with the free standing article (den/det) as well as the ending (en/et). You're right that it sounds redundant - the closest direct translation in English would be 'The white the season', which is kinda weird!
No. This is a feature of Swedish which is called double determinacy. You can even say that the determinacy is triple, since both the article, the adjective, and the noun show determinacy. You can think of it as a kind of harmony between the words, where they all express the same grammatical feature.
There are a few expressions where the article isn't needed. These are special cases that are perceived more or less as names. Vita huset for 'The White House' is one example – if we're speaking about the house where POTUS lives, not if we're speaking about some other white house.
You would not say "Jag vet det svaret" for "I know . The definite article is only used when there is an adjective on the noun. Though - of course - there are exceptions, as Arnauti has mentioned in a reply below.
So to be complete:
Jag vet svaret = I know the answer.
Jag vet det svåra svaret = I know the difficult answer.
Jag vet ett svar = I know an answer.
Jag vet ett svårt svar = I know a difficult answer.
Jag vet frågan = I know the question.
Jag vet den svåra frågan = I know the difficult question.
Jag vet en fråga = I know a question.
Jag vet en svår fråga = I know a difficult question
p.s. Vet/Know here does not mean 'I know the answer to the question' but only 'I know of the (existence of) question'. Again, see Arnauti's comment down for more.
It is actually possible to say det svaret, it means that answer.
On the other hand, we normally use the verb kan with svar and particularly with fråga. There is an important difference in meaning too: if I say jag vet en fråga, that means I know of a question, i.e. I know what the question is, but if jag kan en fråga, that means that I know the question, i.e. know the answer to the question. (it could also mean that I know a certain question by heart, though less likely)
The important thing is that you can not say 'jag vet den här frågan' to mean that you can answer this question. It's Jag vet det här, but Jag kan den här frågan.
amrjunior1 yes, I'm a native Swedish speaker from Sweden. I'm one of the people who helped create this course in the first place and I sometimes hang out here to answer questions.
It is possible to say Jag kan det svaret, it means 'I know that answer'. It's a bit hard to think of a context for this sentence, but it is correct.
Ah yes, det här svaret means this answer. In these constructions there is also a definite article. Again, for completeness sake:
Det här svaret = This answer.
Detta svar = This answer.
Det där svaret = That answer.
Den här frågan = This question.
Denna fråga = This question.
Den där frågan = That question.
De här frågorna = These questions.
Dessa frågor = These questions
De där frågorna = Those questions
Both are the same. They both have a definite article and a definite ending.
Den is the definite singular (common gender) article.
De is the definite plural article
Årstiden is the definite singular form of årstid (which is of the common gender).
Byxorna is the definite plural form of byxa.