and be redirected back to the survey to complete the dependent measures.
That's something that must happen in the external piece of software. It must read the case token, remember it, and the use it for the redirect back.
If the software cannot do that, you'll have to work without its help. That means, you could run the external page in an within your questionnaire, or you might open the external page in a new browser tab, so respondents will return when they close the tab.
They would remain logged into SoSci but be unable to leave the page with the link until the time is up.
That part is easy: Timer: Show the 'Next' Button After a Certain Period of Time
And regarding the random generator. It will just take care to set the proper URL, but first make sure that it works with one page.