I personally would address them together. Then, the more the mercury issues gets resolved, you can reduce your efforts to overcome the other issues. Why? Because getting the mercury out takes time and you don't need to live these issues in the mean time.

Hair analysis... yes, but it's complicated.

Hair tests are basically core samples of a blood tests. Whatever is in the blood is going to end up in the hair over time.

Low mercury in the blood or hair is not an indicator of no-mercury-toxicity. People who don't expel mercury retain it and eventually get sick. These people typically have lower blood mercury (because it's not being mobilized) and therefore lower hair mercury. So, it's very counter intuitive.

More important would be to check for indicators like high calcium or low zinc.

A more authoritative mercury test is the urine porphyrin test.