Comparing liquid "energy" to batteries
I have no idea how to compare/convert wh/kg from/to kg/m3 nor MJ/kg.


First, \$\rm\frac{[kg]}{[m]^3}\$ are the units of density and not related to energy storage. Your source was just giving the density figures to let you double-check the energy density and specific energy values for self-consistency. Converting from watt-hours per kilogram to kilograms per cubic meter wouldn't make any sense.

Second, one hour is 3600 seconds. And one watt is one joule per second. So you can very easily do the math to convert watt-hours to megajoules.