Is it possible to “pause” my link account, meaning to keep it without having to cancel and lose everything, but also without having to pay for it on a monthly basis? This would be during a period of a few months when I would not have access to Internet, after which I’d hope to “reactivate” my account, picking up where I left off.
Downgrading to free member should not be a problem, you can upgrade whenever your circumstances allow it again. You may lose your imported lessons, should you have any. As far as I know all other things remain yours, such as LingQs and lessons. This is a good topic for the “Support Forum”. Do check with them!
SanneT is correct 
You can downgrade to Free then pick up where you left off at a later time.