liver function is not particularly relevant if you're doing injections and aren't taking any anti-androgens like bicalutamide that impact the liver (AFAIK, I'm not a doctor), but you're just looking for normal levels, yes. (For what it's worth I saw a change in my liver enzymes when I took bica, and I ultimately stopped taking it because it wasn't helping my biochemical dysphoria because it doesn't impact the central nervous system much.)
You seem to have the right impression - lots of doctors want E blood levels of 100 - 200 pg / mL, and yeah <50 ng / dL for T sounds about right.
You're mostly looking for estradiol blood test, I don't remember a bunch of tests related to that, just the one. I think an endo I had tested for Sex Hormone Binding Globulin and Free Testosterone separate from just normal T levels, as well as Albumin. He said the SHBG helps interpret the hormone levels 🤷♀️