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#1: It sounds like you're seeing a different behavior?
#2: Yes, system.UnsubscribeLink references the value in Admin > Email
#3: Send yourself a sample email and click the link to arrive at the live page. If it brings you to your unsubscribe page, it's not deleted, if it brings you to your fallback page (set in Admin > Landing Pages), then it may be deleted.
To find the page asset in Marketo, try just searching "Unsubscribe" in Design Studio. Based on the URL you provided, it looks like the standard Marketo unsubscribe page that everyone gets.
On a side note, regardless of whether you use the built in Marketo functionality for this, there are a few important things to make sure your unsubscribes are being recorded in your email reporting, so you can see how many unsubscribes happen for particular emails:
A) The form should have the standard Unsubscribed field on it, rather than a custom field.
B) The URL should still have the URL parameters you see in Admin > Email: mkt_unsubscribe=1&mkt_tok=##MKT_TOK## (without these, the system won't associate the unsubscribe action with the particular email the lead came from).