Are a ferritin level, thyroid hormone, free testosterone level all blood tests? Tests for hair thinning or hair loss.

Yes. All these levels are checked with blood tests.
All blood tests. Ferritin, thyroid hormone, testosterone levels are all blood tests. However, they likely will not help you to determine the cause for your hair loss. In your age group the most likely cause, by far, is genetically related male pattern hair loss.
Not. Directly. Follicle cells will die early, genetics. There are some options, talk to your dermatologist.