Most species of living organisms have double helix DNA, can there be a tesseract DNA? What benefits does this form of DNA have over the common helix form? Will this form of DNA unique to 5 or higher dimensions being?
Short answer: No, there can't be a tesseract-shaped DNA equivalent.
One of the key properties of the double helix that DNA forms is that it is a linear structure: it is a natural format for encoding information, since you can start at one end, read the pairs in order, and then stop when you reach the other end. It can be easily expanded or contracted to match the data you need to encode - just make it longer or shorter.
The tesseract is completely different; it has only 16 natural locations for data-points, there is no obvious start or end point, no obvious way to order the points...
It might be possible to come up with an alien life-form that uses a tesseract for some fundamental part of it's biology, but it's going to have to be so different in the way it functions that it would make no sense to call it 'tesseract DNA'.