We present continuum-estimated (2+1)-flavor lattice QCD results for second-order fluctuations of conserved charges and the leading-order equation of state in the presence of strong magnetic fields at nonzero baryon chemical potential, using the HISQ action at the physical pion mass. The baryon--electric charge correlation $\chi^{\rm BQ}_{11}$ exhibits striking sensitivity to the magnetic field: $R_{cp}$-like double ratios $\chi^{\rm BQ}_{11}/\chi^{\rm Q}_{2}$ and $\chi^{\rm BQ}_{11}/\chi^{\rm QS}_{11}$ reach enhancements of $\sim2$ and $\sim2.25$ at $eB \simeq 8M_\pi^2$ along the transition line, establishing $\chi^{\rm BQ}_{11}$ as a magnetometer of QCD. To bridge theoretical predictions and experimental observations, we construct HRG-based proxy observables and apply systematic kinematic cuts emulating STAR and ALICE detector acceptances, which retain $\sim80\%$ of the lattice QCD magnetic sensitivity. Extending to the QCD equation of state under strangeness neutrality and isospin asymmetry, we determine the chemical potential ratio $q_1\equiv(\mu_{\rm Q}/\mu_{\rm B})_{\rm LO}$ and the pressure coefficient $P_2$ for magnetic field strengths up to $eB \simeq 0.8~{\rm GeV}^2 \sim 45 M_{\pi}^2$. The results reveal temperature-band crossings, hierarchy reversals, and non-monotonic structures driven by the nontrivial interplay between thermal and magnetic effects.