Because "a" would be difficult to distinguish since "andare" begins with the same vowel. Therefore "d" is added to form "ad"
Similar thing happens when you have "e" before a word that begins with a vowel (Donne ed uomini)
The prepositions A & DI are added after some verbs before the infinitive. Provare happens to be one of the verbs that uses A. Here's a good list you may like to use: http://italian.about.com/od/verbs/a/aa031908a.htm I believe the only way to really know these is to simply memorize them... Dnovinc gives a great explanation of why it is AD instead of A as well. Hope this helps. Cheers!
why is wrong city here? I thought città was city. They put town instead of city
I think "in citta" probably translates to the English phrases/idioms "into town" or "into the city/town". Something like "into city" would sound strange to a native English speaker, but would be understood.