Signs of a healthy tank:
apart from those you have mentioned...
An acceptable layer of green algae growth (on the back or sides of the tank). It's really biofilm we want, but I can't see biofilm.
No funky smells
No scum film on the surface
I've come to rely on TDS readings a lot more. It will give me a quick indication of what KH/GH is (Indication only. Still need to test for the real value).
Sometimes I gauge plant health/growth. Specifically for Potassium (K) levels. Plants are not the only ones that need potassium. Apart from Calcium, potassium is the 3rd most abundant mineral in the body. I'll dose my own premix of Ca:Mg:K. Similar to Salty Shrimp, but I don't know if SS uses potassium.
shrimplets and juvies !!
Signs of an unhealthy tank (for me):
Blue Green Algae, Staghorn, or Black Beard Algae
Hair and String algae is not as bad but it's more of an annoyance and can get out of control quickly
Low water movement (low oxygen)
surface scum (low surface agitation and too much iron or protein waste)