Make a Interrupt on a stm32f4xx
Am I right with this calculation ~0x3 = ~(0000 0011) = 1111 1100 ?


Almost, stm32 is a 32 bit processor so it will be:
1111 1111 1111 1111 1111 1111 1111 1100


  So when I do GPIOC->MODER &amp;= ~0x3;, am I setting the first to bits of this register to 00 (input mode)?


For the description of each register you have to look hat this Reference Manual. For the MODER register of PORTC check page 153. It shows that each 2 bit group of the register sets the properties of one specific pin on that port. '00' is for input as stated on the next page.
Your write of GPIOC->MODER &amp;= ~0x3; will result in PC0 being set to input. What you want is GPIOC->MODER &amp;= ~(0x3 &lt;&lt; 26); This will set bit 26 and 27 to 0 which relates to pin 13.


  Should I set other two bits of this register ?


For just this one pin you don't have to write more to this specific register.


  How can I know which two bits of this register are linked with my button ?


On Page 154 it states 


  Bits 2y:2y+1 MODERy[1:0]: Port x configuration bits (y = 0..15)


this give you the relation of pin to bits in the register

[0:1] for pin 0, [2:3] for pin 1, ... [30,31] for pin 15

Note: With pin I mean the pin of a port, not the actual physical pin on the chip.


  Why TIM9 and not TIM10 or TIM11 ?


TIM 9 10 and 11 are all identical. You chose which one you want. STM32s usually have 3 different type of timers (TIM1, TIM2-5, TIM9-11) which have slightly different features. You have to know what you need and which one supports that.


  Finally, I want to enable a clock so I do RCC->APB2ENR |= 0x00004000; : 0x00004000 = 0100 0000 0000 0000 => I set the 16th bit of this register which is "TIM9 clock enable". Is that what we want to do ?


Yes this is part of setting up the timer. This will enable the clock for the timer peripheral so it is able to run at all. Although bit 16 is 0x10000 in hex or 0001 0000 0000 0000 0000 in binary.
The timer will still not run at this moment. You have to do more setup. How you setup the timer is described on page 366 and following.