Is it possible to change the keyboard controls in Emacs Tetris

As far as I know (and I've done quite a bit of reading about Tetris lately), no official version of Tetris changes its piece-selection method as the game goes on.

Assuming you're asking about the NES version, the only difference as the levels progress is the speed that the blocks fall at.

Here is the falling speed for the levels, in the number of frames it takes for each piece to drop one cell towards the bottom. The game runs at 60 frames/second, so a value of 60 would mean it moves down one cell per second, a 6 is 10 cells/second, etc.

  Level    Drop speed
         (frames/line)
     00            48 (0.8 s)
     01            43 (0.72s)
     02            38 (0.63s) 
     03            33 (0.55s) 
     04            28 (0.47s) 
     05            23 (0.38s)
     06            18 (0.3 s) 
     07            13 (0.22s)
     08             8 (0.13s)
     09             6 (0.1 s)
  10-12             5 (0.08s) 
  13-15             4 (0.07s)
  16-18             3 (0.05s)
  19-28             2 (0.03s)
    29+             1 (0.02s)

(source)

For completeness, the randomizer always works as follows:

1. Pick a (pseudo)random number from 0-7, representing the 7 possible pieces and one "dummy number" (7). If it comes up as 7 or the same number as the previous piece, go to step 2. Otherwise, give the piece represented by the chosen number.
2. Pick a (pseudo)random number from 0-6, and give the piece represented by the number.

So there's a lower-than-normal chance of getting the same block twice in a row, but that's about it.

This is kind of a vague question and the primary answer is going to be equally vague: it depends on which Tetris you are playing.

More elaborately, every different version of Tetris will have its own block choice algorithm. The ones I've most commonly heard about are a "true" random generator that doesn't make any kind of judgement, a "fair" generator that generates random sequences of all seven blocks (so you /will/ get every type of block equally often, but the order in which you get the blocks within a 'batch' of six will vary)...

... And then there is Bastet, or "Bastard Tetris", which distinguishes itself by having an algorithm that chooses the worst possible block with malice aforethought.

For further reading I recommend the wiki pages here (different tetris random generators) and here (the 'official' guideline to what makes a Tetris game).