Does the addition of water to N2H4 produce N2H4
Yes, equations must be balanced, thus the only correct way to write this is:

$$\ce{N2H4 + H2O &lt;=&gt; N2H5+ + OH-}$$

Easy to remember: Nitrogen typically has a free electron pair which can act as a Lewis base for a proton.

If your textbook says $4$, it is an error in your book. Good job on spotting it and realising it.