Russian has a lot of French and German influence. Russian royalty and aristocracy were generally Germans. Many times the language of the court was actually French and Russian was sidestepped many times in favour of the West. It is no surprise that titles and pronouns may have French, German or other influences.
It's a fair comparison, because "vous" in French is used both as a formal singular second-person pronoun and as a plural second-person pronoun, formal and informal. The same can be said about Вы; it can be used to address a single person respectfully, or it can be used to address any plural of people, whether formally (like guests to an event) or informally (like friends).
Another example of this is in Turkish, where "sen" is the informal singular "you," and "siz" is either the formal singular "you" or the plural "you" (both formal and informal).
"Sie" in German could also serve in this way, in that it can both be singular or plural, but it is ONLY formal. An informal plural "you" also exists in German (ihr).
This very way, "до свидания". The most common informal version is "пока". Also, it is common to wish well when you part with someone, like "Удачи!" (Good luck!), "Всего доброго", "Всего хорошего" (Have a nice day), etc.
Personally, I prefer "Добрый день/вечер" and "Всего доброго" to "Здравствуйте" and "До свидания". They sound heartier :-)
"Do svidaniya" is mostly used when you are talking to someone who is older than you, for example if you are a teenager you would say it to an adult, if you are 30 years old you would say it to an elderly person. It's basically an expression of respect. However, people don't usually use it when talking to family members or close friends, you don't say it to your parents or grandparents, at least based on my experience.
You are almost right. It's [до сви-дА-ни-я].
When breaking Russian words into syllables, don't break apart a consonant and the following vowel. They are always part of the same syllable.
There's always exactly one vowel in a syllable in Russian. I.e. the number of syllables is equal to the number of vowels.