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They do like a dormancy every now and then. I will include a link at the end for more information.

Now, as for the powdery mildew... There are many effective ways to control this. Neem oil is not always the most effective, but it works most of the time. I recommend using other oils as well. Garlic oil, rosemary oil, and cinnamon oil are very good methods for controlling these infection. Mix a half teaspoon into a spray bottle of water, and spray as often as you need.

This article is on the care of Oxalis: https://www.gardeningknowhow.com/houseplants/shamrock/growing-shamrock-plants.htm

This collection of articles will give you more information on using these oils, and more: https://www.gardeningknowhow.com/special/organic/

This article will give you more information: https://www.gardeningknowhow.com/houseplants/shamrock/growing-shamrock-plants.htm

Even if it is an indoor plant, they will still require a dormancy. You can create this yourself by watering less, and exposing the plant to cooler temperatures and less light.

This article will give you more useful information: https://www.gardeningknowhow.com/houseplants/shamrock/growing-shamrock-plants.htm

This sounds like spidermites. Have you noticed any webbing? You can get rid of this by spraying neem oil. There are many other things that can also work. This link will take you to a collection of article that will give you some more information: https://www.gardeningknowhow.com/special/organic/

These like to have a dormancy each year. They will either die completely or just stop growing for a little while. This is the time to divide this. You don't really have to be careful. This can be an invasive species in some areas, so the risk of killing it is very low.

When you go to split it up, wet the soil, and take it out of the pot. Cut the tops off leaving any tiny new growth. Then rip them into segments. Plant these in their own pots, and you are good to go. It is important to always work with soil when it is slightly moist. It will make things much easier.

As an added bonus, the leaves make a wonderful addition to salads. They have a flavor that is similar to green grapes. A litle sour but a little sweet.

Here is an article for more information on the care of these: https://www.gardeningknowhow.com/houseplants/shamrock/growing-shamrock-plants.htm

When the top of the soil is almost completely dry. This plant can tolerate a wide range of conditions, but it doesn't like wet soil for very long.

This article will give you more information on the care of the plant: https://www.gardeningknowhow.com/houseplants/shamrock/growing-shamrock-plants.htm