Weak equivalence principle, swampland and $H_0$ tension with fast single radio bursts FRB 180924 and FRB 190523

Two new fast single radio bursts FRB 180924 and FRB 190523 well localized to massive galaxies have opened a new window to probe and characterize how cosmic baryons are allocated between galaxies, their surroundings and intergalactic medium. We are motivated by testing Einstein's weak equivalence principle with these two cosmic transients which have accurate redshifts. Using photons with different energies emitted by FRB 180924, we obtain, so far, the most stringent bound $\Delta\gamma<2.16\times10^{-10}$ for non-repeating FRBs with accurate redshifts when only considering the gravitational potential of the Milk Way. If using the gravitational potential of the Laniakea supercluster instead of the Milk Way one, we also obtain the strictest bound $\Delta\gamma<1.06\times10^{-14}$ to date. In light of rapid progress of FRB cosmology, towards the next two decades, we give an universal limitation $\Delta\gamma<8.24\times10^{-22}$ from photons with different energies emitted by single FRBs with accurate redshifts. Moreover, we analyze detailedly the effects of various astrophysical parameters on the precision of weak equivalence principle. We also estimate the abilities of single FRBs with known redshifts to test the validity of swampland criterion, and to distinguish which value of $H_0$ is preferred.