  We present an effective Lagrangian formalism for the calculation of flavour
changing neutral and charged scalar currents in weak decays including
$SU(2)\times U(1)$ symmetry breaking effects and the effects of the electroweak
couplings $g_1$ and $g_2$. We apply this formalism to the MSSM with large
$\tan\beta$ with the CKM matrix as the only source of flavour violation, heavy
supersymmetric particles and light Higgs bosons. We give analytic formulae for
the neutral and charged Higgs boson couplings to quarks including large
$\tan\beta$ resummed corrections in the $SU(2) \times U(1)$ limit and
demonstrate that these formulae can only be used for a semi-quantitative
analysis. In particular they overestimate the effects of large $\tan\beta$
resummed corrections. We give also improved analytic formulae that reproduce
the numerical results of the full approach within $5-10%$. We present for the
first time the predictions for the branching ratios $B^0_{s,d}\to \mu^+\mu^-$
and the $B^0_{d,s}-\bar B^0_{d,s}$ mass differences $\Delta M_{d,s}$ that
include simultaneously the resummed large $\tan\beta$ corrections, $SU(2)\times
U(1)$ breaking effects and the effects of the electroweak couplings. We perform
an anatomy of the correlation between the increase of the rates of the decays
$B^0_{s,d}\to\mu^+\mu^-$ and the suppression of $\Delta M_s$, that for large
$\tan\beta$ are caused by the enhanced flavour changing neutral Higgs couplings
to down quarks. We take into account the constraint from $B\to X_s \gamma$
clarifying some points in the calculation of the large $\tan\beta$ enhanced
corrections to this decay.
