We present a search for the B^+/-_c meson in the decays B^+/-_c ->
J/psi pi^+/- and B^+/-_c ->  e^+/- J/psi X.  We measure the limit of
sigma(B^+/-_c).BR(B^+/-_c -> J/psi pi^+/-)/sigma(B^+/-_u).
BR(B^+/-_u -> J/psi K^+/-) and sigma(B^+/-_c).BR(B^+/-0_c ->
J/psi e^+/- X)/sigma(B^+/-_u).BR(B^+/-_u -> J/psi K^+/-) as a function of the
B^+/-_c lifetime, using \approx 110 pb^-1 of data collected at the Collider
Detector at Fermilab (CDF).  We present also a search for the rare decays
B^0_d -> mu^+mu^- and B^0_s -> mu^+mu^-, setting an upper limit on their
respective branching ratios.