である is a casual form of です。 This is my book. これはわたしのほんです。 これはわたしのほんである。 But we rarely say である in daily conversations. It's seen in books, I think.
にある is 'be in/on/ in front of, etc.' The book is in the bookcase. The book is on the desk. in front of, at the back of … You can tell where the things are with にある。 If you are looking for living things, you say にいる instead of にある.
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