Unfortunately, I don't have any photos to go with but I will try to answer some of your questions and give a little bit of additional advice.
What type of insecticide or treatment you choose to use, depends on a few factors, the type of pest, the type of plants, how bad is the infestation, what is the current state of the plant.
I would suggest to start by only using something that has a label on the bottle meant for use on plants. Just because it comes in a bottle, does not mean it is bad for you or you to use in your home. There are plenty of safe chemicals you can use in your home, like insecticidal soap, pyrtherin spray, & neem oil, just to name a few.
The reason it's important to use something developed for plants is because it has been tested/proven to work. How well it work depends on the the type of pest and how bad the infestation. A label on a bottle will tell you exactly how much to use, how to use it and what pest it is used to treat. It will also list some plants that spray is safe to use on. The label will not list all plants, so it is important to test it on one leaf and leave it for 48 hours or longer to see the results. If it is dangerous to that plant that leaf will show damage.
To treat for pest means using multiple applications. One time spray will not work. You will need to do at least one other follow up spray in 2-4 weeks. In the case of mealybug it is best to use more than one approach.
Pest tend to attack weak plants, plants that are under stress. If you do not water enough or water too often this leaves the backdoor open for a pest infestation. Healthy plants get pest less often than unhealthy plants. Or they are able to still remain healthy even with a few bugs.