When is it available to visit the Abbey? Can one stay a week? What is the cost?

Also, you can make a day visit with no reservations. Just show up.

Check the Abbey website. You can reserve a time I believe 4 months in advance. You have the option of staying 4 nights (begin Monday leave Friday morning), or 3 weekend nights (begin Friday leave Monday morning.) I believe you can do one of each per year. No cost, but donations accepted and well deserved.

Call for availability. One can stay Monday afternoon through Friday morning or Friday afternoon through Monday morning. They ask for an offering but leave its amount up to you.