"Books are interesting."
입니다 and 있습니다 are two different words. 입니다 is a copula, roughly equivalent to English "is", and very similar to Japanese です "desu". 있습니다 means "has", but can also be used to mean "there is".
재미 is closer in meaning to something like "interesting-ness". 재미있습니다 literally translates something like "[it] has the quality of being fun/interesting".
The exact same way! :D Though depending on context, you may be able to swap out the topic particle 은 for the subject particle 이 if you're already talking about the book in question; sometimes you can even leave the word "book" out entirely, if it's obvious from context you're talking about the book.
If it's not obvious from contwxt you're talking about any noun in the plural, you can add 들 to the end (so 책들 specifically means "books", plural) but you don't usually do this unless you need to make absolutely clear you mean the plural.
There's a lot of decent resources out there to help you learn pronunciation. You can copy the text into Google Translate, its Korean text-to-speech is really clear and alternates between slow and fast readings so you can get a better feel for how the sounds fit together.
For the record, Kieran's sound inventory is almost entirely different from US English. So it will take some time to adjust to some of the sounds.