Ytdyklly

With the following code:

arc = Graphics[{Arrowheads[{0, 0.04}], 

    GraphicsComplex[

     Table[{0.5 + 0.7 Re[Exp[I*g]], 0.5 + 0.7 Im[Exp[I*g]]}, {g, 

       Subdivide[0, Pi/2 - Pi/6, 100]}], Arrow[Range[101]]]}];

sensor = Graphics[

   Circle[{0.5 + 1. Cos[Pi/3], 0.5 + 1. Sin[Pi/3]}, 0.03]];

sensorM = 

  Graphics[Style[Text["M" , {1, 1.47}], FontSize -> 18, 

    FontFamily -> "Latin Modern Roman"]];

Omega0 = Graphics[

   Style[Text[

     "!(*SuperscriptBox[([CapitalOmega]), (0)])" , {0.2, 

      1.27}], FontSize -> 20, FontFamily -> "Latin Modern Roman"]];

OmegaE = Graphics[

   Style[Text[

     "!(*SuperscriptBox[([CapitalOmega]), (e)])" , {0.8, 

-0.27}], FontSize -> 20, FontFamily -> "Latin Modern Roman"]];

theta = Graphics[

   Style[Text["[Theta]" , {1.2, 0.77}], FontSize -> 20, 

    FontFamily -> "Latin Modern Roman"]];

rpolar = Graphics[

   Style[Text["r" , {0.85, 1.17}], FontSize -> 20, 

    FontFamily -> "Latin Modern Roman"]];

er = Graphics[

   Arrow[{{0.5 + 1. Cos[Pi/3], 

      0.5 + 1. Sin[Pi/3]}, {0.5 + 1. Cos[Pi/3] + 0.3 Cos[Pi/3], 

      0.5 + 1. Sin[Pi/3] + 0.3 Sin[Pi/3]}}]];

etheta = Graphics[

   Arrow[{{0.5 + 1. Cos[Pi/3], 

      0.5 + 1. Sin[Pi/3]}, {0.5 + 1. Cos[Pi/3] - 0.3 Sin[Pi/3], 

      0.5 + 1. Sin[Pi/3] + 0.3 Cos[Pi/3]}}]];

erUnit = Graphics[

   Style[Text[Subscript[OverHat[e], r], {1.25, 1.55}], FontSize -> 20,

     FontFamily -> "Latin Modern Roman"]];

erthetaUnit = 

  Graphics[Style[Text[Subscript[OverHat[e], [Theta]], {0.75, 1.65}], 

    FontSize -> 20, FontFamily -> "Latin Modern Roman"]];

h = Graphics[

   Line[{{{-1, 1/2}, {0, 0}, {-1, -1/2}}, {{0, 1/2}, {1, 

       0}, {0, -1/2}}, {{1, 1/2}, {2, 0}, {1, -1/2}}}]];

propVector = 

  Graphics[{Arrowheads[{{Automatic, Automatic, h}}], 

    Arrow[{{-1., 0.5}, {-0.5, 0.5}}]}];

lines = Graphics[{Line[{{-0.8, 0.2}, {-0.8, 0.8}}], 

    Line[{{-0.75, 0.2}, {-0.75, 0.8}}]}];

pinc = Graphics[

   Style[Text["!(*SubscriptBox[(p), (inc)])", {-0.95, 0.75}], 

    FontSize -> 20, FontFamily -> "Latin Modern Roman"]];

Show[{Graphics[{Dotted, Circle[{0.5, 0.5}, 1]}], 

  Graphics[Circle[{0.5, 0.5}, 0.5]], arc, sensor, sensorM, Omega0, 

  OmegaE, theta, rpolar, er, etheta, erUnit, lines, propVector, pinc, 

  erthetaUnit, 

  Graphics[{DotDashed, Arrowheads[0.04], 

    Arrow[{{0.5, 0.5}, {0.5 + 1. Cos[Pi/3], 0.5 + 1. Sin[Pi/3]}}]}]}, 

 Axes -> True, AxesOrigin -> {0.5, 0.5}, 

 AxesLabel -> {Style["x", FontSize -> 20, 

    FontFamily -> "Latin Modern Roman", FontColor -> Black], 

   Style["y", FontSize -> 20, FontFamily -> "Latin Modern Roman", 

    FontColor -> Black]}, AxesStyle -> Arrowheads[{0, 0.05}], 

 PlotRange -> All]

I produced the following image

Eventually, I will get rid of AxesTicks, but I leave them for reference. I am puzzled how I can modify the Axes Range. For instance, the x-axis should range from -0.3 to 1.3 and similarly for the y-axis. The AxesLabel should be moved accordingly but the rest of the figure should not be modified.
Thanks in advance!

Remove the axes and add the arrow and text primitives in the desired location:

Show[{Graphics[{Dotted, Circle[{0.5, 0.5}, 1]}], 

  Graphics[Circle[{0.5, 0.5}, 0.5]], arc, sensor, sensorM, Omega0, 

  OmegaE, theta, rpolar, er, etheta, erUnit, lines, propVector, pinc, 

  erthetaUnit, 

  Graphics[{DotDashed, Arrowheads[0.04], 

    Arrow[{{0.5, 0.5}, {0.5 + 1. Cos[Pi/3], 0.5 + 1. Sin[Pi/3]}}]}]},

  Graphics[{Arrowheads[{0, 0.05}], Arrow[{{-.3, .5}, {1.3, .5}}], 

   Arrow[{{.5, -.3}, {.5, 1.3}}], 

   Text[Style["y", FontSize -> 20, FontFamily -> "Latin Modern Roman",

      FontColor -> Black], {.5, 1.4}],

   Text[Style["x", FontSize -> 20, FontFamily -> "Latin Modern Roman",

      FontColor -> Black], {1.4, .5}]}], 

 Axes -> False, PlotRange -> All]

This is basically the same a what kglr posted, but it is structured so that making adjustments to the axis graphics is easy. In particular, using Offset makes very easy to adjust the position of the axis labels, since the adjustment is made in printer's points and thus independent of the coordinate system.

axes =

  Module[{axesLblF, xAxisPts, yAxisPts, xLbl, yLbl},

    axesLblF = (Style[#, 20, "TR"] &); 

    xAxisPts = {{-.3, .5}, {1.3, .5}};

    yAxisPts = {{.5, -.3}, {.5, 1.3}};

    xLbl = Text[axesLblF @ "x", Offset[{10, 0}, xAxisPts[[2]]]]; 

    yLbl = Text[axesLblF @ "y", Offset[{0, 10}, yAxisPts[[2]]]];

    Graphics[{Arrowheads[{0, 0.05}], Arrow[xAxisPts], xLbl, Arrow[yAxisPts], yLbl}]]



Show[

  Graphics[{Dotted, Circle[{0.5, 0.5}, 1]}], 

  Graphics[Circle[{0.5, 0.5}, 0.5]],

  arc, sensor, sensorM, Omega0, OmegaE, theta, rpolar, er, etheta, 

  erUnit, lines, propVector, pinc, erthetaUnit,

  Graphics[

    {DotDashed, Arrowheads[0.04], 

     Arrow[{{0.5, 0.5}, {0.5 + 1. Cos[Pi/3], 0.5 + 1. Sin[Pi/3]}}]}],

  axes,

  PlotRange -> All]

Note: I use the Times Roman font ("TR") because I do not have "Latin Modern Roman" on my system.