Most of this is very well written.

Wedding Video

You could say "I like to film events", or you could say "I like filming events". However you can't just say "I like film events" because when you use it that way "film" is a noun, not a verb.
The rite celebration ceremony is at the municipality of Tivoli with the mayor, and after that we are going to a fascinating villa near by Tivoli.

1/ A wedding ceremony is a type of rite, but you never use that word for a wedding. Generally the word is only used for more primitive rituals, like initiation ceremonies. 2/ "after that" makes the sentence flow more smoothly. 3/ "near" is enough for this type of usage. You use "nearby" when you are describing what is around another place. For example, "The railway station has a chemist shop nearby". In this case however you are just saying that the villa is not too far from (that is, "near") Tivoli.

Before the rite ceremony, I and my girlfriend and I have to go to my cousin's house for some photo shooting and to his wife's house to film "the cutting of the tape" a typical Italian custom!

1/ By convention in a list of people, you always put yourself last in English. "My friends and I", etc. 2/ The word "Photo" is for clarity only. 3/ "Cutting": you would use the gerund (gerundio) version because "cutting" is functioning as a noun here; it's part of the name of the ceremony.

I would like to have from you some advise advice from you about songs to use as the theme song.

1/ Word order, like the positioning of "from you", will become easier with practice. There is no "easy to remember" list. 2/ "Advise" is the verb, "advice" is the noun. 3/ You need an article before "theme song". In this case you could say either "a theme song" or "the theme song". And you're asking the wrong person since my favourites are "Urlando Contro Il Cielo" and "Communque Andare", both of which could be taken the wrong way at a wedding.