Let's talk about 了 first cuz it's simpler. If there was a 了 after a verb, it means the action has happened already. For example, 吃 = eat, 吃了 = ate (or have eaten). 到 ... 去 is like a phrasal verb, you just need to remember it to know how to use it. "到 someplace 去" = go to someplace/leave for someplace; "到 someplace 去了" = went to someplace/already left for someplace. As for the meanings of 到 and 去, what you said in your question is not exactly right. 到 means leaving for some place, 去 means "go". An opposite word to 去 is 来, meaning "come", but 去 and 来 here are not really verbs, they are a little like adverbs (maybe they are, i'm not good at grammar) indicating directions. If you mean Jill left for some place that's not where you are right now, you use 去(go), otherwise you use 来(come). - 他到图书馆去了 (He went to the library.) - 他到图书馆来了 (He came to the library.) (Maybe he's on the way, maybe arrived, but he definitely left the place where he used to be, that's what 了 means here.) Why is 了 immediately after 去 not 到? It's because as I said, "到 ... 去" is a phrase itself, you don't break it.

在这句句子里，你对“到”的理解很对，是指“go”的意思。 “去了”在这里是做tense的作用，stress 过去或者已经完成，所以和“到”是不同的用法。 ex：他去了哪里？where has he been? 他去了图书馆=>he has been to the library. ex：他去哪里了？where did he go? 他到图书馆去了=>he went to the library ex：他到哪里了？他到了图书馆 =>he arrived the library. ex：他到哪里去？where is he going?他去图书馆=他到图书馆去 he is going to the library 希望对你有帮助~ 其实真实口语中： ex：你去哪？ 我去图书馆 ex：你去哪了？我去了图书馆 ex：你到哪了？我到了图书馆

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"去“ and "到...去”means to go，but "到“ means to arrive.You can make this sentence simpler. "他去图书馆了“ is a more concise form of "他到图书馆去了”. "到...去了“ is a oral expression which has the same meaning of "去...了”。 We use“了” to show the tense. Among the four sentence you mentioned above, the first and the fourth both mean "You went to the library." The second one is a wrong sentence. The third means "You arrived at the library."

I'm pretty sure 了 is there to make the sentence past tense. It's like changing "go" to "went" in English. Not sure why they used 到 and 去 in one sentence though. I guess they just like to do that sometimes. How long have you been learning Chinese?