If you can find a priest, yes. If you are Catholic, you can go to Confession during one of the times listed in the crypt chapel's side chapel downstairs and ask the priest to bless your rosary afterwards. You could probably ask a priest after Mass or check if there is a priest on-site (ask one of the workers), like the spiritual director.
I would think before or after the Mass it wouldn't be an issue. It is a warm and welcoming Parish Community
Yes you can get a blessing
I'd imagine yes. They have a large gift shop that is manned so you may what to call them to ask when someone would be available to do that for you.
Yes. There is always one or more priests available.
That hour is the same morning Sunday
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