Spin the Calculator

SOGL V0.12, 70 69 67 bytes

i⅛⁸Νο;⌡░▼Y6γj±²‘1n4n.⌡Iø,→{_≤whwιh:"/*-+”;W? )Κ; (Κ;}+}:Ƨ)(čøŗoļ=→p

Try it Here, or try a version which takes inputs as given in the test-cases

uses SOGLs I operator, which rotates the array. Then reads a string as a JavaScript array, and where an operation is used, encase previous result in parentheses, evaluates as JavaScript and then removes the parentheses.

Dyalog APL, 94 88 86 85 bytes

{o,'=',⍎('('\⍨+/'+-×÷'∊⍨o),'[×÷+-]'⎕R')&'⊢o←(((⌽∘⍉⍣⍺)4 4⍴'789÷456×123-00.+')⊃⍨⊂∘⊢)¨⍵}

Try it online!

Takes the rotations as left argument, 0-3, and the 1-based indices as right argument, as a list of y x coordinates, like (1 1)(2 3)(4 5) etc.

This got quite messy because of the right-handed evaluation of expressions in APL.

C (gcc), 282 294 295 296 300 304 306 310 bytes

All optimizations need to be turned off and only work on 32-bit GCC.

float r,s;k,p,l,i;g(d,x,y){int w[]={y,x,3-y,3-x,y};d=w[d+1]*4+w[d];}f(x,y,z)int**z;{for(i=0;i<=y;i++)putchar(k=i-y?"789/456*123-00.+"[g(x,z[i][0],z[i][1])]:61),57/k*k/48?p?r+=(k-48)*pow(10,p--):(r=10*r+k-48):k-46?s=l?l%2?l%5?l&4?s/r:s+r:s-r:s*r:r,r=p=0,l=k:(p=-1);printf("%.3f",s);}

1 byte thanks to @Orion!

Try it online!

Function prototype:

f(<Direction 0-3>, <Number of entries>, <a int** typed array in [N][2]>)

Input format (as on TIO):

<Direction 0~3> <Number of entries>
<Entries 0 Row> <Entries 0 Column>
<Entries 1 Row> <Entries 1 Column>
....
<Entries N Row> <Entries N Column>

Ungolfed version with comments:

float r, s;
k, p, l, i;
g(d, x, y) {
  int w[] = {
    y,
    x,
    3 - y,
    3 - x,
    y
  };
  d = w[d + 1] * 4 + w[d];
}
f(x, y, z) int **z; {
  for (i = 0; i <= y; i++)
  {
      putchar(k = i - y ? 
      "789/456*123-00.+"[g(x, z[i][0], z[i][1])] : 61),     // Print character, otherwise, '='
      57 / k * k / 48 ?                                     // If the character is from '0'~'9'
        p ?                                                 // If it is after or before a dot
            r += (k - 48) * pow(10., p--)                   // +k*10^-p
        :
            (r = 10 * r + k - 48)                           // *10+k
      :
          k - 46 ?                                          // If the character is not '.', that is, an operator, + - * / =
            s = l ?                                         // Calculate the result of previous step (if exist)
                    l % 2 ?                                 // If + - /
                        l % 5 ?                             // If + /
                            l & 4 ?
                                s / r
                            :
                                s + r
                        :
                            s - r
                    :
                        s * r
                 :
                    r,
                    r = p = 0, l = k                        // Reset all bits
          :
            (p = -1);                                       // Reverse the dot bit
  }
  printf("%.3f", s);
}

The code can handle cases such as 1+.7 or -8*4.

Very sad C doesn't have an eval .