Where does the CPU get its first instructions from? In order for the BIOS code to matter, it must be evaluated by the processor. However, the processor itself needs to do work to actually get access to the BIOS code, since the CPU only performs instructions that are given, something must give the instructions to the CPU (since I can't imagine a way for instructions to just "flow" from BIOS to the CPU without anything in between).

Where are the instructions for loading BIOS and passing control to it stored, and who passes these instructions to CPU so that CPU can preform them?
1. (A summary of the answer-in-comments by Jukka)

Startup code is stored in ROM (non-volatile memory) at a fixed address X.

When you activate the "reset" signal in the CPU, the CPU will initialise its registers to certain hard-coded values. The instruction pointer is one of these registers that are initialised to certain hard-coded values. In essence, the CPU manufacturer picks this hard-coded address X. 
Hence, when you reset your CPU, the instruction pointer is reset to the same fixed address X. The CPU starts to execute instructions as usual: fetch the next instruction from address X, decode it, execute it, etc

Then whoever puts together a complete computer has to make sure that there is something useful at address X (e.g., a ROM memory chip with meaningful startup code).

2. Elaboration

The CPU has a very simple way of working, known as the FETCH-EXECUTE cycle:  

(a)  FETCH: It goes to the memory and brings the instruction that
 is at address [PC].  (PC is a name of an internal CPU register; it
    holds the address of the instruction we need to perform next..).
(b) Execute: The PC executes the instruction it has just
    retrieved from the memory
(c) PC $\gets$ PC+1.(*)
(d) Go back to (a).  

This fetch-execute loop happens all the time, regardless of the program you are running. In particular, when the CPU boots up (say, when its power goes from 0 to Vcc) the CPU simply begins to perform the above loop. 

The initial value of PC depends on the specific CPU. It can be that the CPU wakes up with PC=0, or it can be that PC=0xFFF0 (as happens with Intel's X86 family), or with any other value PC=$PC_{init}$. 
If you press the reset button, or turn the power off and on, the CPU  restores the PC to its initial value $PC_{init}$ and the CPU begins running the program that is in the memory at address $PC_{init}$, through the fetch-execute loop.

Now it is the computer designer task to make sure that the BIOS sits in the memory at address $PC_{init}$. The BIOS usually resides in a non-volatile memory so there is always a program to run in that address, even if you just turned the power off and on (this deletes the RAM but not the BIOS. It is more difficult to delete/change the BIOS, although possible and happens, e.g., when your device updates its "firmware").


(*) Advancing the PC by +1 assumes that each instruction takes 1 address of the memory space. The is rarely the case. In real systems we may see here PC+4 (as in the 32b MIPS) or PC+x (with $x\in\{1,...,7\}$ which depends on the instruction itself) as in the X86 family, etc.