Please help us help you and fill where relevant:
Your LimeSurvey version: [ LimeSurvey Cloud
Version 5.3.13]
Own server or LimeSurvey hosting: LS hosting
Survey theme/template: bootswatch
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(A caution warning is shown at the begining of my questionnaire ("Caution: Javascript execution is disabled..."). Is there any way to remove this ? Thank you. Is there any way to disable alert throughout the Survey?)

If the detectionroutine has no bug, the warning will stay until you use a browser where JavaScript is working. LimeSurvey is not working 100% without JavaScript.
I recommend to try a different browser to check if the message will vanish.
If not, you can report that as a bug via the bugtracker.