The decay constant should be given in SI unit which is s-1. The formula is 0.693/T.
Decay rate or rate of decay is activity. If the activity of a source is 10 s-1, simply mean 10 atoms decaying in one second. If each decay gives off 5.25 MeV , the power of the source is P = A(Energy) = 52.5 Mev per second.
