I never had a normal TSH when I was on methimazole. When my T4 and T3 were in the normal range, it was always suppressed. This is known as subclinical hypertyroidism. My endo wasn’t concerned at the time – just based my methimazole dosage on my T4 and T3 levels.
After I got my TT, this changed because my T4 came from a tablet and TSH is the hormone my body was producing. My endo wanted my TSH to reach the normal range. We finally got it there, but it took a lot of time and 5 levothyroxine dosage reductions.
Regarding hair loss, I never had a problem when I was on methimazole, but I started gradually losing it a couple of years after my TT.