If you do not earn your course certificate within 180 days, your registration will expire and you will need to pay to re-enroll for the course.
On this Coursera page it is mentioned: “If you want to pause or suspend a subscription temporarily, you'll need to cancel your subscription, then re-start it when you want to return. All your work will be saved, but your personalized deadlines will re-set when you resume your paid course access.”
In response to this need, Coursera has developed a suite of academic integrity features that will help institutions deliver a high level of academic integrity by 1) deterring and detecting cheating and 2) accurately assessing student mastery of the material they're learning with private assessments.
No, you will not get certificate of completion if you complete a 7-day free trial of any course in Coursera. For getting a certificate, either you have to pay the required course fee or you have to apply for the financial aid.