HAT, Servo, and STEMMA QT SHIM Compatibility?

[JJMoney]

I have three components needed for my project:

1. NEMA-17 Stepper Motor
2. Servo Motor
3. Time of Flight STEMMA QT Distance Sensor

I am working with a Raspberry Pi 3 Model 3 V1.2. This is my first RPi project, so I want to be sure everything will work as expected before I buy all of the components.

My current plan is to control the stepper motor using this DC & Stepper Motor HAT. According to this pinout.xyz diagram, the HAT will only occupy GPIO pins 1, 3, 5, and 17. Therefore, it seems a 5V power pin, a ground pin, and a GPIO pin are all still available for the servo to connect to.

However, to use the distance sensor, I am thinking of using this STEMMA QT SHIM. This raises a few questions:

1. Will the SHIM be compatible with my other components since they're also using pins that the SHIM needs as well (namely pins 1 and 5 for the HAT and pin 2 to power the servo)?
2. Even though the HAT occupies all of the RPi's ground pins, can the other components still use these ground pins as well at the same time?
3. Under the assumption that all of the components can work at the same time and I use the extra tall stacking headers, will all of these components fit?

If powering the servo externally would help, that is also an option.

Thanks in advance!

[adafruit_support_bill]

Power and ground pins can be shared by multiple devices.

And the i2c bus pins (SDA & SCL) can be shared by multiple i2c devices. The only limitation is that each device on the bus must have a unique i2c address. https://learn.adafruit.com/i2c-addresses/the-list

[JJMoney]

Power and ground pins can be shared by multiple devices.

And the i2c bus pins (SDA & SCL) can be shared by multiple i2c devices. The only limitation is that each device on the bus must have a unique i2c address. https://learn.adafruit.com/i2c-addresses/the-list

Thank you so much for your help. I'm not sure if this will impact my project, as the only device I'm using mentioned in the page you linked is the stepper motor HAT. This being the case, it seems as though my setup will work just fine.