I'm trying to understand the structure behind the sentence.
(我)看電影可以學中文。
Does this sentence translate roughly to "I can learn Chinese while watching a movie". Shouldn't this use 一邊, or is there a structure here that implies 'while'?
EDIT: I just realized, is this Topic-Comment structure? 我可以學中文看電影 » 看電影，(我)可以學中文.
看電影 - watching movies
可以 - can
學中文- learn Chinese
看電影可以學中文 (watching movies can learn Chinese。) = You can learn English by watching movies
Similar structure:
打工 - working part-time
可以 - can
賺學費 - earn tuition
打工可以賺學費 (working part-time can earn tuition) = You can earn tuition by working part-time
Shouldn't this use 一邊, or is there a structure here that implies 'while'?
The [一邊 X 一邊 Y ] structure mostly refers to two separate actions
Example:
一邊看電影一邊學中文 (watch movies while learning Chinese) could mean you are watching any movies(not Chinese movies) for entertainment while studying Chinese
"(我)看電影可以學中文"
Example sentences with 我可以...:
我可以藉/靠看電影(去)學中文 - I can rely on watching movies to learn Chinese.
我可以經由看電影(去)學中文 - I can learn Chinese through/by watching movies.
我可以一邊看電影一邊學中文 - I can learn Chinese while watching movies.
Does this sentence translate roughly to "I can learn Chinese while watching a movie".
I wouldn't say it's "while" (as in "at the same time") and so 一边……一边 would be inappropriate, but instead "through" or "by means of"---the method of learning Chinese is watching movies. Also, I don't think the omitted subject is necessarily 我 (e.g., a Chinese teacher might also say this to their student), but this depends on context. Chinese is often like this, where you're left to infer omitted pronouns and conjunctions.
I'd consider the sentence as short for something like:
通过看电影，我们可以学中文。
So we might say in English:
By watching movies, it is possible to learn Chinese.
You can learn Chinese by watching movies.
(where the "you" doesn't refer to an actual person, but is the informal version of "one" in the sense of "one can learn Chinese").
The grammar seems close to a topic-comment sentence; the 看电影 ("watching movies") describes the scope of the sentence (I think this would be classed as an adverbial 状语), and in that context, we say 可以学中文 ("it's possible to study Chinese"). It's a bit different, however, because the topic 看电影 is a verb phrase.
基本的句子结构是：主语+谓语+宾语，同英语一样。
"看电影"是一个动词短语，这里名词化了，做主语，表示一种行为，看电影这种行为。
"可以学"是谓语部分，可以是一个副词，修饰动词学。
"中文"是宾语，"学"这个动作的对象。
