Kutya bevihető a fellegvárba.

try to find the renaissance restaurant at the bank of Danube, they can help you to call a local taxi with which you can go to the castle for approx 2500 huf

There is some entry fee, the view is the best from the castle, however a round tour is also possible.

Kb. 15- 20 perc. ( A kisgyerek lehet ugye "hurcibában", vagy csatangolhat is - tehát passz.)

I have asked my son who lives in Visegrad. We hired a car but I know there are a lot of inexpensive buses.

Hi, The Citadell is part of it originally, but that is he best view spot there in the area so they chagre for going up to the tower. Once it is worth going there so you see it, but there is a spectacular view anyways from every spot around there. As I grew up in Bp and have seen it many times (long time ago it was free to go up the Citadell), I would not pay for it, but as a tourist I would recommend to do so once you are there. I don't know about the shuttle bus, always walk up there, it is a nice about half an hour scenic walk. But I am sure there is a public transport bus as well, but I do not know the number as I do not live in Hungary anymore. Here is the website for the public transport of Budapest, you can check everything how to go to which place. There is an official link to the public transport company of Budapest, but I cannot link it in. Put BKV homepage into your google search and it will come up. They give you details and even route planners. Good luck and enjoy the city :)

Sorry I have no idea :(