Problem:
Some parameters in URL weren't being missed when switching language (or visiting translation).
Solution:
If you are using "Language name added as a parameter" option and want to preserve other query string parameters across translations, make sure to turn on the following setting:
WPML -> Languages -> Language switcher options -> Preserve URL arguments
And add the parameters separated by a comma.
After adding just move out of that box, so it is saved automatically. Then reload the page in frontend and you can see the parameters added to the language switcher or the target URL.