"I borrowed a new book from the library and read it."
"Te" puts "karite" in sequence with "yomimashita". Two basic rules for such sequences are 1) that they are always in order of occurrence and 2) the tense or state is found in the final verb in the series. (The borrowing happened before the reading and both actions are now completed.) This is not all there is to know about these series but it's probably enough for now.
I entered "図書館から新しい本を借りて読みました。" and got it wrong. Does using kanji cause problems with accepting answers?
I think duo hasn't "registered" all kanji yet, you know? All kanji that were already taught are accepted, and some of the most common ones. At least for now, probably they'll add more with time.
I did the same and it happened to me also (and I see that this is 6 months later...) I have started reporting this. (I am hoping that at least it will help the developers see which sentences need more kanji added to them so that the slightly more advanced learners can get their answers accepted...)
Can anyone please explain to me why is it "借りて読みました” in the end?
When you string multiple actions one after another you have to use this construct. We want to say "borrowed and read it". So we use "borrow" in it's て form and then "read" in its tense-appropriate (past in this example) form. So, if in future you will need to put multiple actions together, you need to use all of them-1 in て form, and the last one in a tense-appropriate form.