Hi Koushik,

Use Epilog rather than GridLines.

P1 = BodePlot[TF1,
  PlotLayout -> "Magnitude",
  PlotStyle -> Directive[Green, Thick],
  Mesh -> {{{-3}}, {{16659.759374487337}}},
  MeshStyle -> PointSize[Large]]

P2 = BodePlot[TF2,
  PlotLayout -> "Magnitude",
  PlotStyle -> Directive[Orange, Thick],
  Mesh -> {{{-3}}, {{5377.124388436974}}},
  MeshStyle -> PointSize[Large]]

epilog1 = {Green, Dashed, 
   InfiniteLine[{{Log10@16659.759374487337`, -25}, {Log10@16659.759374487337`, 0}}]};

epilog2 = {Red, Dashed, 
  InfiniteLine[{{Log10@5377.124388436974, -25}, {Log10@5377.124388436974, 0}}]}

Show[P1, P2, Epilog -> {epilog1, epilog2}]

I don't understand the second part of your question. If you want to add additional horizontal or vertical lines or points, add them to the Epilog.