Are all instructions eventually converted to zero-operand instructions?
This will depend on the computer architecture.  zero-operand computer architectures use the stack, so to add 2+2:


PUSH 2 (into the stack),    
PUSH 2 (again),  
ADD (call the instruction - note that no operators are passed by).
POP ( 4 out of the stack)


but most other computer architectures e.g. use registers, memory addresses and values as the parameters to an instruction (in addition to the stack). For example the same 2+2 in a CISC computer.


MOX AX,02 (AX=0)
ADD AX,02 (AX=4)


However, if you're thinking in terms of translating a high level programming language into executable code e.g. one routine calling a subroutine the list of parameters most likely be passed by via stack and the number of parameters be reduced to 0 as in the first example.