If you use utm_medium cpc, the traffic will get bucketed into the Paid Search default channel grouping in GA.
If you use utm_medium cpm or display, then that traffic will get bucketed into the Display channel in GA.
See the below definitions for channel groupings in GA (ignore the red highlighting, it's from another context):
As per your observation, to ...
You need to add your Google Tag Manager code in your website.
Then, you have two options:
Leave it, don't do anything else. Your Google Analytics code will remain as it is and FB Pixel will be added via Google Tag Manager.
Alternatively, you can remove the code for Google Analytics from your website and add a tag in Google Tag Manager https://support....
you can leave the global site tag tracking code snippet on your site, just do not also configure tags for GA pageview tracking within GTM.
If it were me, I would remove the global site tag tracking code snippet and configure tags for GA tracking within the google tag manager container.
Bit of extra information:
Both Tag Manager and gtag.js perform ...
To answer your questions:
Why adding facebook pixel code reduces the score on gtmetrix?
The reason the Facebook pixel reduces your GTMetrix score is because it is an additional script with a short caching time, and GTMetrix's algorithms give better scores when you have fewer scripts and they have longer caching times.
How can I solve this problem?
Have you checked the loading time of your site with and without Facebook pixel? Isnt't that the problem? If you check this WP Rocket article, it also mentions that such tracking methods can have effect on site speed, thus cause worst grade on metric sites: https://wp-rocket.me/blog/how-third-party-tags-and-trackers-impact-website-performance/
If we are ...