Rotate every row and column in a matrix
CJam, 13 bytes

{{a.m&gt;1m&lt;z}/}


An unnamed block (function) that takes the matrix and the list on top of the stack (in that order) and leaves the new matrix in their place.

Run all test cases.

Same idea, same byte count, different implementations:

{{\(@m&gt;a+z}/}
{{(Im&gt;a+z}fI}
{{:\Im&gt;]z}fI}


Explanation

Ideally we want to treat each instruction in the list the same, and just use it to rotate the first row of the matrix. This can be done quite easily by transforming the matrix after each instruction a bit and making sure that all those extra transformations cancel out in the end. So after processing each instruction, we rotate all rows one up (such that the next instruction along the same dimension processes the next row) and then transpose the matrix, such that we're actually processing columns next. These additional transformations are orthogonal to the instructions in the list and have a period of exactly 2n, just what we need. 

As for the code:

{      e# For each instruction...
  a    e#   Wrap it in a singleton array.
  .m&gt;  e#   Combine it element-wise with the matrix to rotate right. This is
       e#   a fairly common idiom to apply a binary operation only to the first
       e#   element of an array, since element-wise operations just retain all the
       e#   unpaired elements of the longer array.
  1m&lt;  e#   Rotate the rows one up.
  z    e#   Transpose.
}/