Sorry to hear you lost some shrimps!
How big is your tank and how long has it been running? Did you do the 'cycle'?
When doing a water change you should drip the new water into the tank. That will illiminate the temperature difference problem and any difference in parameters between the two waters.
When acclimating new shrimps you should drip acclimate them as long as you can, the longer you do that the better chance they have of survival. You will need to match the water temperature to that of the tank by floating the container with the shrimp in the tank once you have stopped dripping, before adding the shrimp to the tank!
The parameters you have I would think are acceptable so I would stick with tap water if that is what you are using, for now. RO water is ideal but you will then need to buy GH/KH+ to add the minerals. As I say, I would hold off using RO/distilled water for now until we can pin point the problem.
If your water has a green tint to it that may be an algae bloom? A white tint is usually a bacteria bloom and I have only seen that whilst a tank is 'cycling'. I think an algae bloom will mean there is less oxygen in the water as the algae absorbs it??????
Overfeedinng is very common. It will depend upon the size of the tank and how long it has been running etc. With only a few shrimp there may actually be no need to feed additional to the natural biofilm of the tank. As shrimps are feeding all day on biofilm it is usually better to see additional food as just a treat and feed very sparingly. Overfeeding with shrimps doesn't usually mean that the shrimps over eat, it usually means too much uneaten food polutes the water and if you have green tinted water, algae bloom, that may be why? There usually comes a time, if you are lucky, that there are too many shrimps in the tank for the biofilm to sustain on its own, so as the population grows feeding may become more necessary.
Shrimp don't usually hide unless they are new to the tank or there are fish etc (even then they will usually adapt to them) or as JayC says, their is something wrong with the water quality?
Simon