My premium membership ended yesterday (5/28/14) but I still have the gold medal on my profile and I can watch subscriber videos.
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You have access for as long as your login cookie is good for (30 days from since you last logged in). I'm not sure how intentional this is, but I'm sure the good will it has generated and will continue to generate is worth having a few people game the system for an extra month.
From what I have noticed in the past, when your sub ends there is normally a "grace" period before you lose full access. This has happened to me before when I didn't realize my sub was coming up for renewal.
Yep. This isn't a bug. There is a short grace period in order to give people an opportunity to renew without losing access.