When you set the timer, have the tank lights on when the residents are most likley going to be viewing the tank. So maybe come on around noon and off at 9 or 10 pm or something. The schedule doesn't really matter, so long as there is a period of darkness.
Any of the swordtail or platy varieties will be fine together, they all came from the same basic wild fish species. Select different colours for variety.
I'd forgotten about the GH, thought this was hard water. Yes, put some dolomite or aragonite fine gravel/sand in the substrate, or find a substrate that is calcareous. I can't help much with this as I have never had this issue. I have very soft water and keep only soft water fish.
On the cycling, this is a case for a good bacterial supplement. Dr. Tim's One and Only is probably the best, but the Tetra SafeStart is good (it is actually Dr. Tim's original formula), and I have used Seachem's Stability. Follow directions on the label of whichever. With lots of live plants one doesn't need this, but live plants are going to add too much trouble in this situation.