How to access the programming assignments after completing the course?

Yes, the assignments are behind the paywall. There is a topic about that on the FAQ Thread, although it’s a little late for that now.

If you want your personal copies, I don’t know any way other than subscribing for one month. Then download everything before that one month expires, so that you don’t have to keep paying. And I guess there is no guarantee that they don’t delete your files when you unsubscribe. Sorry, but the mentors don’t have to deal with the subscription process so I’m not really sure how it works. You could ask Coursera. Try clicking the small blue square ? lower right on any of the course pages to get to Coursera Help and see if you can find an answer.