PWM FAN controller & Ideal 24V DC to DC 5V Converter just to feed 556 IC
The proposed schema to control a 4-wire fan is NOT in spec. 

You need to read and understand the specification for the 4-wire fan you are using. 

Probably the best historical document describing the fan spec was produced by Intel on Formfactors.org, that site is long gone but you can get the document here.

In this document the PWM freq is stated as 21-28kHz and the PWM drive signal MUST be an open collector/Drain drive (in other words a pullup resistor or active pullup was NOT permitted). The voltage on the PWM pin was no more than 5.25V, but this was set by the fan ....not the driving elements. In some fans avaialble today, if you actively pullup the PWM pin or connect to two fans you get the wrong speed. Most of the early fans had a limited low speed range too, with 20-30% full speed not unusual.  

Things have changed over the years and many fan manufacturers have improved their specifications. One example here for the Delta fans which can use a PWM freq of 30Hz- 30kHz, tolerates active pullup and 10V PWM amplitude.
Arctic fans are another example, with their own specification for multiple fans (up to 4) on one PWM signal line. 


  Your proposed PWM fan control


I would suggest that the operation using a 556 timer may have problems. 


You are using active pullup, which may not work depending on the fan.
You mention using 16kHz which may not work depending on the fan. 
Your freq and pulse width controls will interact.
T1 does absolutely nothing. I think perhaps you meant to create a CC source with T2, but what you have does not work that way. At high temperatures you may find T2 is turning on sufficient to reset your 556. If you are depending on simply the R3C5 time constant your timing is way out, T2 may be on for 8-10 Tau. 


As a suggestion you may be better to design a solution based on an ATTiny85 driving an AO3400 or AO3402 for the PWM output. It would be a lot less components and board space. 
The ATTiny would require about the same current (12-15mA) as you might use for the 556 timer so a small SOT-89 78L05 would be adequate to power the MCU. 

Update:
Since the OP has now posted details of the fan being driven, it's possible to show some of the hazards to not following the 4-wire fan spec.   

The fan is a Sanyo-Denki 9BMC24P2G001. The datasheet has little detail of the PWM signal, but the Catalog shows on page 551 the following information on the PWM signal:



Clearly from this information you can see that providing an active pullup may actually damage the PWM signal input or in your case would simply shut down the +5V regulator. The only way to drive this type of input is open collector/drain. To use active pullup you would require either a series resistor to limit current or a series Schottcky diode.  

Update_1:

The new circuit is a vast improvement over the old one, with just a few comments:


If you want to drive multiple fans then simply add more AO3400 FETs





It appears you want to switch between an internal Pot and an external Pot. I would suggest the following change to ensure safer wiring and predictable failure modes.




With the circuit above you don't feed +5V into your wiring, so it's safe from short circuits.
Using two A/D inputs allows you to easily separate both the function and scale of the external versus internal Pot.
Providing a limited scale for the pots means you can detect an open circuit wire, or a faulty pot.

I have no idea what your intent is for this piece of the circuit: