  We discuss production of charm quarks and mesons as well as nonphotonic
electrons in $pp$ scattering at RHIC. The distributions in rapidity and
transverse momentum of charm and bottom quarks/antiquarks are calculated in the
$k_t$-factorization approach. The hadronization of heavy quarks is done by
means of fenomenological fragmentation functions. The semileptonic decay
functions found by fitting semileptonic decay data measured by the CLEO and
BABAR collaborations are used. Good description of the inclusive data at large
transverse momenta of electrons is obtained and a missing strength at small
transverse momenta of electrons is found.
  Furthermore we discuss kinematical correlations between charged leptons from
semileptonic decays of open charm/bottom, leptons produced in the Drell-Yan
mechanism as well as some other mechanisms not included so far in the
literature. When calculating the Drell-Yan processes we include transverse
momenta of $q$ and $\bar q$, using the Kwieci\'nski parton distributions.
Reactions initiated by purely QED $\gamma^*\gamma^*$-fusion in elastic and
inelastic $pp$ collisions as well as diffractive mechanism of exclusive $c \bar
c$ production are included. A good description of the dilepton invariant mass
spectrum measured by the PHENIX collaboration is achieved. Predictions for the
dilepton pair transverse momentum distribution as well as distribution in
azimuthal angle between electron and positron are presented.
