Re: Why did Noam and/or Shimon choose to communicate as a 4, 4-bit composition?
It is simply a very common convention to organize bit sequences in groupings of four to make them more readable for humans. It's directly analogous to the difference between writing
12345678 vs 12,345,678
The leading bit is not the opcode -- it is merely a flag that indicates which type of instruction it is.
For A-type instructions there is no opcode (or you could consider the flag to be the entire opcode)
For C-type instructions, the 7-bit combination of the a-bit and comp bits are essentially the opcode, though you could include the jump bits and/or the leading 1 bit with some justification. Traditionally the opcode excludes immediate values or bits that indicate source and destination locations.