"I have been learning Chinese for a year. I'm still a beginner."
Subj. + Verb + 了 + Duration + 了 is the chinese contruction to express a duration of an ongoing action.
there should only be one of the 'le's. having 2 isn't necessary or correct (my keyboard doesn't have Chinese, sorry)
This structure: verb + 了 + time duration + 了 shows the duration of an ongoing action.
No that's not correct. At least one need to be used in spoken Chinese, but in written Chinese you need them both.
It's very important about the using of 了, as Chinese is a Analytic Language.
my guess is：the first 了 is for past tense and the second is used for emphasis
This is the most awkward way possible to express having studied Chinese for a year. Most people would simply say something like 我学了一年的中文
I don't think that your suggested sentence specifies that the year of studying Chinese has been this past year (up to and including the present). Your sentence could refer to a year of Chinese study that happened a decade ago, whereas the sentence structure in this lesson specifies the duration of an action that is still ongoing.
You should cut the sentence as "我，学中文，学了，一年了” Of course we say "I have been learning Chinese for a year." in English, but we do need 学了 to make it more natural. In other words, you can take 学中文 as object and 学了 as verb, so you can understand more easily.
Common grammar. The second typically indicates a degree to which something is done
Because 中文 should come right after the verb, but 了 should also come right after the verb. Chinese accomplishes this by repeating the verb!
I find it really evil they've separated 中and 文，what is the actual benefit in that apart from making life difficult for people. Honestly this course needs a LOT of work and should be marked as in beta, because there are a ton of mistakes and unaccepted answers still.