The combined relativistic energy approach and relativistic many-body perturbation theory with the zeroth order ab initio model potential optimized one-particle representation are used for precise computing the energy levels and radiative decay probabilities (radiation amplitudes) of heavy alkali elements, in particular, there are listed data for the 7s 1/2-np 1/2 , 3/2 , np 1/2 , 3/2-nd 3/2 , 5/2 (n=7-10) transitions in Fr and some E1 and E2 transitions in a single ionized Hg + atom. The comparison of the calculated values with available theoretical and experimental (compillated) data is performed..