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As long as it is from the same source you drink from, it should be safe for your plants. It is very common for people in drought areas to turn to using "grey" water, which is basically the water they just used for washing dishes, bathing, etc in the house. This sounds like it is no different and should not be harmful to the plants.

The only thing I can think you will want to check is when you say filtered, is the water also softened? Softened water can cause issues with plants. This article can explain:
https://www.gardeningknowhow.com/plant-problems/environmental/softened-water-and-plants.htm

Not usually, unless perhaps it is done during the hottest times or most intense sunlight time of the day. The water droplets can act like magnifying glasses and burn the leaves, thus taking away some of the ability of the tree or plant to thrive as it should. I like to wash the foliage of the plants, shrubs, roses and trees as I water them in the early morning or in the evening once the temps have cooled down. It helps open the pores on the leaves and allow them to function better.

This article should help: https://www.gardeningknowhow.com/ornamental/trees/tgen/watering-newly-planted-tree.htm

Ideally, the best time to water is either early morning or early afternoon. But, if you have forgotten to water them and they are drooping, ASAP is best.

Too little irrigation will stress the plant and possibly cause issues with IPM. A plant stressed for any reason is more susceptible to pests and disease. Soil fertility should not be affected by too little irrigation. If the plant is stressed by lack of water, it will not be able to use feertilizer correctly. If the plant is wilted, fertilizer could burn root tips.

Check with your local water department or agricultural extension office to see if they can test your sample. Check Amazon or eBay...or your local garden center for a test kit.