Oh oh! Inorganic chemistry question! Hooray!
Concepts such as formal charges can basically be thrown away when we're talking about coordination chemistry in general. Bonding with d-block metals is typically more a complicated affair than in organic molecules. Formal charges a nice shortcut and they help explain reactivity in simple terms but they're not always applicable to coordinate complexes.
In early inorganic classes they generally teach these bonds are dative, basically the metals centers are very electron efficient and only the ligand donates electron density toward the metal-ligand bond. That's not typically true though, there is quite often covalent contribution from the metal's d-orbitals especially if the metal in question is more electron rich (late d-block metals) and if the ligand has orbitals of similar energy to accept the electron density (such as thiols, phosphines, or carbonyl).
As for why water would bother to do this in the first place, we'd have to take a look at molecular orbital diagram of a relevant complex. I assume you'll eventually learn this (if I assume you'll be taking any upper level inorganic classes) so I'll just sort of lay out the general idea. Basically by interacting with the d-orbitals of the metal centers the energy of the metal center's orbitals can be lowered thus forming a more stable species. The benefit is mostly for stabilizing the metal rather than the ligand.
And to answer your last question there, it actually shouldn't be too surprising to see water "give/share" to another atom. Remember water itself will hydrolysis into hydronium and hydroxide spontaneously, in which the oxygen gives some of its electrons to a proton. A metal center is much more electron efficient than a proton and we would expect water to bind to it as well.
I like inorganic chemistry...