It sounds natural to me. A student asks me a a question in class and I say, "Use your book to find the answer." It isn't just reading; they might be looking up something in the index or table of contents. It could be finding something on a timeline or in a caption (like in a Social Studies book). Broadening that, perhaps someone has a nonfiction book and I just need a quick answer - I am not going to ask if I can read their book, because that implies I want to read a lot of it. I am going to ask if I can use their book for a minute.
"using" a book, to me, less so refers to simply "reading" it and more trying to accomplish a task by reading it. Like, I would use a book to help me study, someone might use a recipe card while they cook, or as someone pointed out, creatively, they're "using" the book to balance a table, etc. lol
Yes and no. Many people do, others don't. It's quite common to merge the sounds when one word ends with an r, and the next starts with an s. In this case, I'd say it mostly depends on how much you actually articulate the r in använder. If you don't, there's no reason to merge the sounds. But most people do, so it's quite common.
We got it from Middle Low German, though it's a common word in modern (high) German as well - anwenden.
It's from wenden meaning "turn", plus the prefix an- that was used to denote a goal of some sort. We have the same verb (vända) and the same prefix (an-) in Swedish as well.
In Swedish, we do know that it's her own book here. sin can only point back to the subject in the same clause.
So where the English sentence She reads her book is ambiguous – she could be reading her book or some other girl's book, the Swedish sentence Hon läser sin bok is not – it's always her own book. If she reads another female person's book, we say Hon läser hennes bok. And if she reads 'his' book, we say Hon läser hans bok.