si puoi portare il cane nel parco che circonda il monastero, non in chiesa o all'interno del chiostro

I don't believe so as you pay at the entrance which is quite a distance from the Abbey and church. You might want to email them and request early entry for the outside grounds as they may allow it if the gate area is manned.

Durante la mia visita nn ho visto animali e nn c è nessuno che possa accudirli da ciò che ho potuto osservare

i can't write the website of monteolivetomaggiore but ... OPENING HOURS Standard Time: 09.15 morning – 12.00 Afternoon 15.15 to 17.00 Daylight Saving Time: 09.15 morning - 12.00 Afternoon 15.00 to 18.00 Sunday morning's closing at 12.30 The Abbey entrance is free. The groups that have their guidance can move independently. The number of the guide Abbey is: Dino Benincasa 0577.718567 (meal) For further information cali directly to the Abbey at: 0577.707611 Visit the Nativity of the Abbey The visit to the Crib is possible at the following times: From Monday to Saturday morning: upon request Saturday afternoon: always open Sundays: always open except from 10:15 to 12:00 because of the Mass

per raccogliere l'acqua piovana

Yes should be possible. Church might be closed for service if you arrive at a certain time.

No dogs inside, unfortunately, but they can circulate outside

I believe our visit was on a Tuesday with Roberto. I remember the pickup was early morning, perhaps 8 or so? It was part of a full day of touring.