The grid pattern is a glitch with the render engine, to get rid of it use Yafray.
Water continuously is easy; select the object you have set up for a fluid and go into the fluid options. Instead of having it as Fluid, instead click Add. That will make it continuously add fluid to the simulation.
Excellent, thanks. I’ll have a go at using the Yafray renderer. My intention is to try and export the fluid simulations to use them in LightWave, so in the long run I’d be using that renderer.