How to insert Google Tag Manager code into pages with variable account value
you should use these two modules:

https://www.drupal.org/project/google_tag

https://www.drupal.org/project/datalayer

First one installs GTM on your page, second one enables passing many variables and taxonomies to be passed to dataLayer. It also has an alter function, if you'd like to add some extra data (since the module is written in a general way and i.e. extracting taxonomies from json arrays on the GTM side can be complicated).

User Id is part of default data added to dataLayer by data layermodule on each page, so you'll have it there.

Regarding your noscript part, you'd have to alter the module i think.