Tannins, caffeine and colour compounds don't flood out of a teabag all at once — they diffuse out of the leaf matrix over time, fast at first and progressively slower as the leaf's easily-reached surface material runs out, approaching a maximum the same way a hot drink approaches room temperature. That's genuinely the same mathematical shape as Newton's law of cooling, and it's why "one more minute" matters far more early in the brew than it does after five minutes have already passed.
Published extraction studies find CTC (crush-tear-curl) teabag tea reaches roughly 95% of its maximum strength by around 7 minutes. A standard teabag in a 200ml mug brewed for 3 minutes sits at about 72% strength — a genuinely different cup than the same tea left for 5, at 88%.
Teabag tea is typically CTC-processed — crushed, torn and curled into small fragments with far more exposed surface area than whole or lightly-broken loose leaves. More surface area means faster diffusion, which is exactly why this tool uses a slower rate constant for loose leaf.
Not the rate — but it raises the ceiling. More tea relative to the water means more extractable material available, so the same brew time reaches a darker maximum, even though the underlying diffusion rate per leaf fragment is unchanged.
Colour is what you actually judge a cup by — this tool solves the extraction equation backward, working out exactly how long your specific tea amount and mug size need to reach the shade you tapped, rather than you guessing at a generic "3 minutes" that assumes a specific ratio.
No — milk is added after brewing and only dilutes the final colour and mouthfeel; it doesn't slow or speed up extraction from the leaf, since by the time it's added the tea and leaves are usually already separated (or the bag removed).