Most of the T4 and T3 in your blood is attached to various proteins. That is called "bound" T4 or T3 and is measured in a Total T4 or Total T3 test . A tiny amount is not bound and that is called "Free" - that is what is measured in a Free T4 or Free T3 test.
In many ways, you can think of Total T4 and Total T3 tests as being related to how much of the binding protein you have rather than a useful thyroid hormone measurement.
However, when you see reference to a T4 or a T3 test, you simply do not know which test it is - Total or Free. You have to look further - check the reference ranges, the results, the units.
The intention of taking levothyroxine is to restore your thyroid hormone levels. Unfortunately, if you take a small dose of levothyroxine, it can reduce the amount your own thyroid makes but not provide enough to make up for that reduction. We see a lot of people who don't do at all well on 25 micrograms, or even 50 micrograms. Some do much better when they take more - maybe 100 micrograms.
Osteoporosis has been seen in people with very high T3 levels - such as occur in Graves disease. There is no evidence that ordinary, sensible amounts of levothyroxine will cause osteoporosis. There is evidence that sensible levels of thyroid hormones improve bone health.