The first question asked how water causes lightning in eruption columns, and whether this is similar to meteorologically generated lightning in thunder storms.
The boiling of water in plumes and consequent rapid disruption of water molecules causes them to shear (or break-apart) this can create a charge which is more positive in larger molecules and more negative in smaller molecules. In eruptions including seawater, the salt included becomes negatively charged. This process discussed is different to the thunderstorm charging mechanisms. However a paper by Williams and McNutt (2005) does propose that the thunderstorm charging mechanism may occur in volcanic plumes (particularly at volcanoes located at high atltitudes with ice). To my knowledge thunderstorm charging is to do with collision of particles and how fast these
It should be stressed that there is not one 'correct' reason for lightning charging in eruptions and it could well vary from plume to plume dependent on a variety of factors!
The second question asked how lightning in a volcanic plume is used to infer height.
There is an excellent overview of this located here. The Met Office (UK) has used this during the eruptions of Eyjafjallajökull and Grimsvotn. Research has found that the number of lightning strikes per hour (or the amount of activity) increases proportionally with plume height. Therefore a rough plume height can be inferred.
I hope this helps!