One of my clients has hired a SEO company, and they want to add "Pixel Code" for tracking website viewers that view the website. I assume that the SEO company will provide me with the required code.

Where does it get added - head, footer? Every page?

Are there any precautions I need to know so the website doesn't blow up in my face?

As far as I understand the code goes into the body of whichever page they want tracking (facebook also have something similar)

As to the dangers,,,, who knows

Yes - Wayan is correct. The code goes in the body, and Google prefers it to be at the top of the body code.

I took an easy way out - I added the Google Pixel code in the same HTML Element that has the Coffee Cup Menu Builder code, and copied the block to all the other pages.

Works like a charm, and no hiccups.

It would be much better to use Google Tag Manager to store the pixel.
You can have as many as you want in there and it will not slow down the page loading time.
It is something else to learn.

Have fun!