What makes a model applicable? It has to 1) make a prediction that is measurably different than a simpler model. And 2) you have to be able to compute what the model predicts. Quantum mechanics, at least the QM theories that are presently useful, are true as far as we know everywhere except in very strong gravitational fields. But as the system gets larger, QM fails on both 1) and 2). How large, and which one fails depends on the experiment. Model a baseball with QM and you'll get answers indistinguishable from Newtonian mechanics. But even single atoms are too complex to analyze if you want to predict their magnetic properties (I may be out of date on that one. It was too hard 20 years ago).
But there are glaring macroscopic effects that need QM to explain. Here's a photography related one - How does light partially reflect from glass? Say 94% of the light gets through and 6% reflect. How does a photon decide? Newton knew that he didn't understand what was going on. What does "understand" mean in this context? I could say that partial reflection is a property of glass and that would be a perfectly good model. But quantum electrodynamics is a simple (to set up, not to calculate with) model of light and electron interactions that predicts perfectly well all optical properties of glass.
As for 100% true, no model is 100% true, although not every model has actually been observed to fail. OK, General Relativity on a cosmological scale is confusing. Dark matter and dark energy may just be error terms. We don't know. The Standard Model (the name for the quantum field theory which accounts for all forces except gravity) has no observed problems. Yet GR and the SM are not compatible. They can't even be defined simultaneously. And if they could be, bad things would happen on extraordinarily tiny scales.
I hope I haven't just confused you more,
Matt
BTW: Feynman's short book "QED: The Strange Theory of Light and Matter" is possibly the best physics book ever written. The glass reflection example is from there. It requires very little math, but cuts no corners on the physics. If you have ANY interest in quantum mechanics, get a copy!