calculations are unreliable in treating most high $T_{c}$ superconductors, since as a rule $LDA$ *underestimates non-local exchange-correlation effects and overestimates charge screening effects* - both effects contribute significantly to the $EPI$ coupling constant. As a result, $LDA$ strongly underestimates the $EPI$ coupling in a number of superconductors, especially in those near a metal-isolator transition. The classical examples for this claim are: (*i*) the $(BaK)BiO_{3\text{ }}$superconductor with $T_{c}>30$ $K$ which is $K$-doped from the parent isolating state $BaKBiO_{3}$. Here, $LDA$ predicts $\lambda<0.3$ and $T_{c}\sim1$ $K$, while the theories with an appropriate non-local exchange-correlation potential [@Yin-Kutepov-Kotliar-PRB] predict $\lambda_{epi}\approx1$ and $T_{c}\sim31$ $K$; (*ii*) The high temperature superconductors, for instance $YBaCu_{3}O_{7}$ with $T_{c}\sim100$ $K$, whose parent compound $YBaCu_{3}O_{6}$ is the Mott-insulator [@Kulic-PhysRep], [@Ma-Ku-Do-Advances].

After this digression we consider the main subject of the paper - *the role of the* $EPI$* with forward scattering peak (*$FSP$*) in pairing mechanism* of the $1ML$ $FeSe/SrTiO_{3}$ (and also $1ML$ $FeSe/TiO_{2}$) superconductor(s) with high critical temperatures $T_{c}\sim(50-100)$ $K$. In that respect, numerous experiments on $1ML$ $FeSe/SrTiO_{3}$ (and also on$1ML$ $FeSe/TiO_{2}$), combined with the fact that the $FeSe$ film on the graphene substrate has rather small $T_{c}\approx8$ $K$ (like in the bulk $FeSe$), give strong evidence that interface effects, due 