A couple of things.

Anything in large enough quantity can be harmful.

I’m not sure how old you are but dawn has been around since the 70s. As a product dish soap as a whole has been around since the early 1900s. I highly doubt that your mother was using engine degreaser in the kitchen in the 60s, 70s, 80s, etc.

To reiterate in case it wasn’t clear. A couple of drops of dawn or a store brand liquid soap in a large spray bottle of water will not hurt you or the plants. It will suffocate and kill the flies which is what you want. It’s also a really easy way to kill flying things that you can’t catch when they get in your house.

Take a minute and think. You wash dishes with it and send down the water pipes either direct into the ground or returned to the city to process and reuse. Dawn is used to clean oil off birds when it spills.

This is true.

Yeah, a little dawn or similar in a spray bottle works as well. When you start seeing shit like this you need to take care of it asap. They can spread and destroy other plants and even neighbors plants.

Probably white fly larva. Spray the plant down with hydrogen peroxide watered down by about 3:1 at a minimum. Alternatively you can buy some oil based sprays (neem and others, iirc) that protect against mold, fungus, white flies, etc.

Doubtful. Coffee, tea and caffeine in general have health benefits when consumed in not extreme dosages.