What is the bonding type in hydrides of group 2 elements?
There is a quite extensive chapter about hydrogen and its compounds in Holleman and Wibereg's book "Inorganic Chemistry". As I only have the german version, I will briefly summarise what I read.

You are of course right, hydrogen forms salt-like structures with alkaline and earth alkaline elements, except for beryllium. Compounds like $\ce{LiH}$, $\ce{NaH}$, $\ce{KH}$, $\ce{RbH}$ and $\ce{CsH}$ crystallise in a sodium chloride structure. Every cation is coordinated by six hydride ions and vice versa. The compounds $\ce{CaH2}$, $\ce{SrH2}$ and $\ce{BaH2}$ crystallise in a fluorite structure. The hydride ions are tetrahedrally coordinated by four earth alkaline cations. The cations are cubically coordinated by eight hydride ions. This &beta;-structure is persistent at higher temperatures. Below $780~^\circ\mathrm{C}$ ($\ce{CaH2}$), $855~^\circ\mathrm{C}$ ($\ce{SrH2}$), and $598~^\circ\mathrm{C}$ ($\ce{BaH2}$) it changes to the &alpha;-form, i.e. the lead dichloride structure. The magnesium compound exists in a rutile structure. Hydride ions are trigonally coordinated by magnesium ions. The cations are octahedrally coordinated by hydride ions.

However, according to the difference in the electronegativities, you would expect a predominant covalent character. The maximum is $1.3$ for $\ce{CaH2}$ and the minimum $1.0$ for $\ce{MgH2}$, which translates to a maximum $30\%$ and minimum $18\%$ ionic contribution. Maybe this is where the statement of the question originates from. Experimental findings rather support the more ionic nature of the compounds though, i.e. the found lattice energies were supported by calculations assuming a purely ionic structure.

The conclusion of this according to Holleman and Wiberg is that the elements are fused by ionic bonds with covalent contributions. The latter increases from $\ce{CsH}$ to $\ce{LiH}$ and from $\ce{BaH2}$ to $\ce{MgH2}$. The magnesium hydride is already borderline covalent.

The question about their reactivity towards water is mainly answered in the chapters for the elements itself. Magnesium reacts readily with water and releases hydrogen. Because of this it is sometimes used as a drying agent. $$\ce{MgH2 + 2H2O -&gt; Mg(OH)2 + H2 ^ }$$
The other elements react similar. The reaction is highly exothermic, the reaction of calcium hydride releases $228~\mathrm{kJ/mol}$. It is often used as a drying agent for gasses because of this feature. Strontium and Barium also react exothermic, i.e. they release $177~\mathrm{kJ/mol}$ and $172~\mathrm{kJ/mol}$, respectively.