Feel free to think whatever you like but I can assure you those are indeed bugs, not any kind of fungal organism. Mealy bugs are an extremely common pest on houseplants regardless of where you live - you are just as likely to have them appear in NY as you are in CA!!

Read up on them. There are many helpful publications that detail these pests and lots of online images to compare to confirm identification. Many species are quite tiny, can be easily wiped off and can be almost dust-like when airborne.

The systemic will not kill your plants. It is a product that is intended for precisely this purpose and is used by many indoor gardeners to kill off all manner of sucking insect pests. The hydrogen peroxide will have a similar if somewhat less effective method of approach.