How can I study animals at my current age?

There is nothing stopping you from doing your own research with animals, the libraries are full of literature, and there are a great number of reputable web sites devoted to the study animals.

You exclude spiders, likely out of fear, but I became fascinated with them 50 years ago, and been studying them since, one of my favorite animals. Arachnology is a very interesting study, and I wouldn't exclude it from your studies.

Wildlife experts are hard to come by these days you have a great opportunity, Godspeed.

Start with easy things like birds, bugs and such. Keep journals, get books to help you identify things and learn how to do that. Learn to sit quietly and watch for hours, taking notes on the behavior of the animals, then compare that to what you read about how they behave. Later, start volunteering a rehab centers for wildlife, or with a conservancy group like The Nature Conservancy to help with bird banding, bat counts, horseshoe crab monitoring, etc. Have fun!