Yes, you can walk around the citadel at night, in fact it is a lovely time to see it, as there are no tourists around. The lights of various towns can be seen on Gozo which is also great to see. We wandered up there after dinner and saw three people, one was the security guard. Obviously things will not be open.

Certo che si...autobus+traghetto+autobus e viceversa al ritorno

You drive up the hill, just past the Citadel and there is a dirt lot at the top of the street. Park and a short walk down the hill to the visitors center or just walk up the ramp into the Citadel.

Reference should be ok but check with the agent. He should have given you a phone number. Or ask your hotel to check.

I am sorry. I was there on a week day. You can walk around all days but I don´t knwo about the museum.

I am not sure about the museum. I haven´t seen there any dog in the area at all. It is al newly renovated and most of the area is on open air.

Access to the Cittadella is 24/7, there is no time when the entrance is closed, what is closed at night are the Cathedral, the shops and museums. Unusually for many places the Cittadella remains lit all night until sunrise, it is a great place to visit in the small hours of the morning when everyone else is fast asleep